Unfortunately, this boat has sailed. The addition of clearly defined actions like "Study" and "Influence" clearly communicates that they're trying to strip away all the need for DM adjudication and turning the skills system into some kind of predefined buttons for the players to push.
It is the DM's game though.
Sure, the players are also there, but that doesn't mean players and DMs are equal.
Of course, you are entitled to your opinion, but the idea of running a game on democracy sounds utterly ludicrous to me.
Owning your game and enforcing your rulings is not the same as being a tyrant.
People sometimes forget that the Dungeon Master isn't jut a storyteller, he's also a referee and has the final say in every matter related to rulings at the table.
It's your game. Own it.
I have watched Perkins running Storm King's Thunder and it was really good.
Instead of slavishly sticking to the rules as written, he instead relied on DM fiat and strong adjudication based on the current fiction.
That's how the game is supposed to actually work. People just forget or pretend...
On the other hand, if we're going for the more sane interpretation, people are only Invisible while out of everyone's sight.
If that's the case, what's the point of being invisible in the first place?