Yes. Provided it was programed with the ability to do so by a GOOD DM in the first place.
Regardless, any player who encounters that program in the future is going to have the same set of experiences, with no variation, regardless of how validated those experiences make them feel.
It's not just about that but... those are like 2 reaaally important DMing skills that not everyone bothers to pick up.
I don't really think there are objective measures of dungeon mastery. I think there are excellent dungeon masters who are mechanical experts, master storytellers, talented world builders, or gifted people managers. I don't think anyone succeeds at all four perfectly, and I don't think competency in all four is necessary to be a great dungeon master. Ultimately, the only metric that matters is whether or not your players respond positively to your style.
Several things here. If you fudge, your players won't earn a thing. You are the one that's choosing when they succeed and when they fail. Their characters don't have input in the resolution of your encounters. You're just playing with yourself. Let the guy who's a "super climber" (or the wizard who prepared Spider Climb or whatever) defeat the wall encounter in an objective manner if they are able.
This is the first pitfall folks encounter when discussing this with me. If you tie the act of fudging to a single roll, it always appears inadvisable. There is no right time to fudge. I am the first person to agree. Fudging is a devastating responsibility that should never be undertaken lightly, for instance simply to allow a player to succeed at a task where they would otherwise have failed. That is counter to the rules and spirit of the game.
The problem is that the game has no single rolls. Every roll exists in a continuum of events, some of which involve rolling and some of which don't. Let me give you a more nuanced example.
Your PCs are negotiating the release of a prisoner. The captors are hostile, but the party's bard is talented both in terms of the player's natural abilities and the numbers on their character sheet (normally, I'd point out the former is irrelevant, but since the numbers don't contradict, it's fine to let them flex a little player aptitude). You're having a good session, and you feel like you've held your own -- the captors' leader has been unreasonably tough but receptive to the bard's generosity and etiquette.
When there have been close calls, rolls have been made throughout the exchange, which has gone on for the better part of a session. Some rolls have gone in the favor of the captors, others in favor of the party. None of them have been finally decisive (and none of them have been fudged). Your social players are eating it up, but your more combat-minded players are starting to wonder when they're going to get to flex some muscle. You're at a strong climax, and it is time to wrap this up.
You decide the captors are willing but not eager to release their prisoner, after considering all the build up, and set a hard-earned Persuasion DC of 15. You keep this to yourself and tell the bard's player to roll one last time. Their final result is a 14.
All things being equal, that is a failure. Two hours of intensive roleplay and strategy are wiped away in an instant of random number generation. Fortunately your campaign is well designed, and this does not derail you or your players. Still, while the loss of time and effort might be mitigated for your martially inclined players as they grin and draw steel, it is keenly felt by your roleplayers and particularly by the bard. Everybody gets XP, but there is a sense of a lost opportunity that was thought to have been bought and paid for.
Or maybe there isn't. Or maybe there is and you and your players are fine with that. These are also valid perspectives. But that's really my point: fudging isn't about changing a number on a die, it's about perspective. It's about recognizing what your players want and need and considering that as a part of your practice.
It's about recognizing that your Persuasion DC of 15 is itself arbitrary and subjective, and that if it is a better choice /for your table/ for you to actually have settled on a DC of 14, acknowledging that you are not infallible is a rational and fair response. If it is a better choice /for your table/ for the bard to ultimately succeed after this long and challenging endeavor, you have the ability to make that choice rather than passing the buck to poorly playtested rules written by people you have never met and numbers "randomly" generated by badly thrown and shoddily manufactured plastic blobs.
Because let's be honest, here. No part of this is objective. We create scaffolding to generate the appearance of objectivity, but it's built on sand. The creators of the game have bias, the dice have bias, your players have bias, and you have bias (even if you are not acting on it consciously). Ultimately, what this diagreement comes down to is that I don't see any value in bias that does not improve the enjoyment of my players, so if I am going to be biased anyway -- and indeed, it is unavoidable -- I might as well be biased in the way that seems most productive to me.
That would be an actual accomplishment.
This is the second pitfall. Why is the situation you describe an accomplishment? Because the player rolled high? Because you set the DC low? Certainly, there are roleplaying games where character creation has a greater impact on success at individual tasks than the die roll, but D&D is only one of those games at higher level, where bonuses start to become ludicrous, bounded or not. Even a +5 bonus is virtually meaningless in the face of a 20-point swing, with results ranging from a superhuman 25 to an unremarkable (and almost certainly failing) 6.
Player decisions and actions matter in the long haul, averaged out over time and countless interactions, but not on individual rolls -- which bolsters my point. Sacrificing the "objectivity" of a single roll to enable an outcome just as often can enhance and support player agency as it can negate it.
But if you're looking for the big enemy of player agency, it's not DM fiat, it's the dice.
I love pre-planning complex sessions and complex encounters. I also love improvising and coming up with things on the fly. I am, however, very forward with my players before we begin a game on the subject of what type of game I'll be running.
This is absolutely paramount. You should never fudge at a table where the players are not comfortable with you doing so, and you should always be honest about your intentions. Likewise if you let the dice fall where they may -- I have certainly had players who would have bowed out upon hearing such a declaration.
But I will say that when I encounter players who object to fudging, I advise them to find another table. I consider dungeon master fiat a duty, not a privilege. My players trust me to make their game great and to make their game /theirs/, and I don't have faith in the ability of my lumpen dice and barely edited sourcebooks to do that for them.
Your PC will either climb the wall or not based on the needs of the plot as perceived through the DM's eye, not by her sick climbing skillz.
This is tangentially related to my first point, but bears special notice. What makes you think that I know what the needs of the plot are? I don't know what's going to happen next in my campaigns. That's up to the players. I have undoubtedly planned for a few possible outcomes, but why would I help a PC up a wall to an end that isn't mine to decide?
What's relevant about deciding whether to fudge a specific roll -- and again, I want to be clear that there is no "right time" to fudge, so please don't mistake me -- is whether it is /necessary/ to save the /moment/ for that player, and for the party as a whole. It is common for detractors to cast fudging as a function of railroading, something a dungeon master who ought to be writing a novel rather than running a game does, but I don't see it that way. It's entirely about people, not about plot. It's about seeing what is needful in the now, and standing up and kicking ass instead of phoning it in.
Does fudging impact the future? Of course it does -- every roll in a session affects the next roll, that's what makes this hobby great and what makes the responsibility of sitting behind the screen so damn devastating. You have to be so careful when you bend the rules. But if you don't bend the rules at all, I could replace you with a CPU. In all cases. And I don't believe that's why any of us are here.
tl;dr: Rule 0 has spoiled us as DMs. You don't need rule 0. It robs the players of their agency.
Couldn't disagree more completely. Thank you for engaging!