I don't think this actually conflicts with what we're saying. In fact, I strongly believe in "roll then narrate" AND "narrate then roll". And I'm not sure I can explain exactly where the line is between the two, but (as I love to say) the existence of dawn does not disprove the difference between day and night. If a players said, "I'm going to pretend to stumble, then pick up sand and throw it in the bandit's eyes, then attack while he's distracted!" I'd let him roll, and if he hits he's free to describe that as being successful (roll-then-narrate). If I've introduced a particularly challenging monster that I've described as having especially sensitive eyes, and described the fine, powdery sand, then I'm going to give him advantage (or something) on the roll (narrate-then-roll).
One thing I don't believe you have answered, Hussar, is my hypothetical scenario about the players that just want to sit in the tavern...in the sense that they don't actually narrate where they go and who they talk to and what they search...and just want to roll Investigation to solve the mystery without having to describe any actions on their part. I'm intentionally choosing an extreme case, of course, but that seems to fit the description of how you play: you aren't requiring the players to figure out likely leads, you are letting their characters do it.
I don't think you would actually do this (would you?!?!) and if not, why not?
Is it possible we play the same way, but we just draw the line in different places?
EDIT: And maybe the difference, now that I think about it, is that the players are free to embellish the world with descriptions of their own, but doing so will not gain them mechanical advantages. If they want to use the descriptions provided by the DM they are more likely to gain the advantage. That probably doesn't provide a definitive answer in all cases, but it's closer.
Why not? 5e comes with downtime activities. If the players came to me and told me, hey, this is what we want to do - can we just resolve this in a couple of rolls after a week of downtime, great, go for it. Why would I force them to dance through my adventure?
Now, I'd probably be pretty annoyed that I've dropped all sorts of adventure hooks and the players are completely disinterested in it, but, let's ignore the obvious issues of table mismatch for a moment. We'll presume the table is happy and healthy, but, they simply don't want to do this investigation thing. Ok, great.
I mean, we do this with all sorts of things - abstract away buying magic items in 3e is a perfect example. 5e does it through downtime. In our current Dragon Heist game, the players actually literally sat in their tavern while their factions went out and gathered information for them. They leveraged their faction memberships and asked the factions to chase down various leads while they stayed home and ran their tavern.
I let time pass and then presented them with the findings.
So, yeah, to answer your question, I honestly have zero problem with letting the players abstract away an entire scenario (in this case it would be tracking down witnesses to a crime, talking to survivors of that crime, checking with law enforcement, and a few other goodies as well - I'm being deliberately vague because spoilers. Chapter 3 Fireball of Dragon Heist if you know the adventure). I presented them with the information after the fact and they proceeded from there. Did I roleplay out contacting each faction contact, then roleplay out the investigations? Nope, not in the slightest. They abstracted it, I gave them the results.
Now, in this specific case, no rolls were needed, but, again, I wouldn't have a problem if they made some sort of checks. Perhaps a Charisma check or something. Heck, they have Faction Scores. A check modified by that would have worked as well, had I thought of it at the time. I didn't think of it, but, in retrospect, that would have been a better idea. A check results in various levels of the faction being motivated to help, which in turn results in various bits of information becoming available. Ah well, will do better next time.