Ok, if I'm reading this correctly, what you are saying is essentially that if a player finds an "exploit"...a weird edge case in the rules, or an unanticipated synergy between abilities, or simply the use of an ability in a setting in which it wouldn't logically work...the 4e resolution is to let the player use the exploit, and the 5e resolution is to have the DM say, "Sorry, that's just not going to work in this case."
Is that a fair summary?
Not remotely. To use non-D&D examples, I'm talking about the difference between a game like Vampire:The Masquerade and a game like Dungeon World. 2nd ed AD&D is more like V:tM (down to the point of endorsing the same "golden rule", that the GM may supsend the action resolution rules at any point in the interests of "a good game). 4e is more like DW.
5e is more ambiguous than any of the above-mentioned systems, but on balance seems to me to be closer to the 2nd ed AD&D/V:tM end of the spectrum.
While in practice I found this to be true, this is not actually true by the rules. See D&D 4e Rules Compendium page 9 where it says the DM can override the results of a check for the good of the story. Further, in the section on skill challenges, it talks about how skill checks should never be a substitute for what the DM thinks is good roleplaying. Further, there is a blurb in one of the books that talks about how the DM can say a power simply doesn't work in a given fictional situation. (I can't recall which book this is, but it's a thing. I've had this discussion before with regard to D&D 4e. Perhaps someone else recalls it.)
You are correct about the 4e RC. It is different in wording from the 4e PHB: here are the two extracts (PHB p 8, RC p 9):
* Adventure Builder: The DM creates adventures (or selects premade adventures) for you and the other players to play through. . . .
* Referee: When it’s not clear what ought to happen next, the DM decides how to apply the rules and adjudicate the story.
* Adventure Builder: The DM creates adventures, or selects published ones, for the other players to experience. . . .
* Referee: The DM decides how to apply the game rules and guides the story. If the rules don’t cover a situation, the DM determines what to do. At times, the DM might alter or even ignore the result of a die roll if doing so benefits the story.
At the time I posted that the RC wording (adventures as an "experience" rather than something played through; the GM not only "adjudicating the story" but also suspending the action resolution mechanics "to benefit the story") was a retrograde step from the point of the overall design logic and play of 4e, and I still take that view.
The issue of adjudicating fictional positioning and the use of PC abilities is more subtle. To give a non-D&D example, in Marvel Heroic RP before a player can successfully declare an action (say, the use of strength to rip a streetlight out of the ground and clock a bad guy over the head with it) the GM has to be satisfied that the action declaration is "credible" given the abilities of the PC. (The example given is credible for the thing, but probably not Captain America.) HeroQuest uses a similar "credibility test", with genre considerations as the main constraint (so if Joe the cowboy has a speed rating of 17, and his horse has a speed rating of 8, Joe's player is nevertheless not permitted to declare, as an action, "I try and outrun my horse", unless the genre is weird and wacky westerns).
In my 4e game I also use a theme-and-genre credibility test, with the tiers (heroic, paragon, epic) being the main guide, as these position the PCs in the fiction relevant to the main antagonists and background characters (temporal rulers, demon lords, gods etc).
But in all these systems, once the credibility test has been applied the DCs are set based on a table (for 4e, HQrevised and DW) or via a mechanically determined opposed roll (for MHRP), And to the extent that the game is properly designed (and I posted an example upthread where 4e breaks down at the upper end), the players have a known chance of succeeding at this DC, as well as a resource suite to bring to bear in pursuit of that.
I think 5e could be drifted in this direction, but I'm not sure that it starts there.