You insist that you are asking genuine questions, that you aren't hostile, and that you want to understand how I see things, but the way you're managing yourself here leads me to question your intent.
Exploration is the give-and-take of the players describing what they want their characters to do, and the Dungeon Master telling the players what happens as a result. You seem to find it incredulous that I'm of the opinion that covering an entire scene with a single adjudication shortchanges the give-and-take.
I don't find it incredulous, so much as I just don't understand what you're saying. My intent is to understand what your position is.
There has been some back and forth with multiple people on this issue, some of whom explicitly said that you seemed to be speaking for them. So I've probably been extrapolating multiple users' positions onto yours whenever I run into apparent gaps in understanding. I'll stop doing that now. Let me back up a little.
Other people definitely claimed that multiple skill checks to resolve an action were a bad idea. Here, you almost seem to be saying the opposite: that resolving an action with a single check is shortchanging the give-and-take?
There's also been some mixed messages over words like "action" and "scene" and things like that. And the examples we've been playing around with involved different situations which may or may not have been full scenes, or single actions within a scene, or perhaps small clusters of actions within a scene.
Since it seems like I'm coming off as aggressive, rather than pushing you to clarify your position, I'll just try to clarify mine:
I think that any given scene will require a variable number of actions to resolve it, from 1 to infinity. A given action, stated by the player, may or may not involve uncertainty and so may or may not require dice be involved at all.
If the DM believes uncertainty/dice is involved, then he may call for one or more checks.
I think the only break down we would have so far is that you would say that at this stage he should just be asking for one check. Right? One action declared -> one check?
In theory that may be well and good, but in my experience, one action is not always really one action. This is perhaps where you would say the player needs to be more specific?
Maybe that answers it, but I'm not totally convinced. For one thing... I don't like my players to be cagey and try to approach a goal in a staccato/baby step "I do this... and also this... and then this." fashion. I'd rather they state their intent as well as their initial action.
Partly this is because I prefer to let players narrate their own stories as much as possible... so laying a sequence out, determining the failure points upfront, rolling for them, and then narrating the outcome all at once, often has a lot of appeal to my group.
So that's one reason to potentially roll several checks in quick succession.
Another reason could be, as the OP originally discussed, because two skills represent two different but complimentary approaches to a problem (e.g. autopsy.) If the PC is taking that approach, I wouldn't have any problem determining the respective success/failure effects and having them make multiple rolls.
Sorry to continue using the autopsy example, but I think it's a good one. I get that you think Medicine would have no bearing on an autopsy. I don't really know how to respond to that, except to say that I disagree wholeheartedly. I don't see how your quotes support the position, and it seems absurd to me. But if I could think of an example you would like more, I would do so.