Since When Did First Time HCs Have a Say in Finding a GM Become a Trend?

No, you tell your people, you tell everyone that will listen that you want that job, but only if you get what you want. You dont tell the hiring manager a damn thing. You work connections to get the info to the bosses boss to make it happen. And if you get that Info to Tony Khan(or whichever owner) it happens.

Or more likely they say, "Pound sand. I'm going with another candidate".