I know I said I prefer Payton, but I can't disagree with anything you said here.

Stauskas was the "get better now" pick and with Cousins ready to dominate, I can see why they went that direction. It's also a little over-simplified to say we don't need a SG because we already picked McLemore. We watched Ben play all of last season, Bill and Jalen didn't. It's clear he's still got a lot of work to do before you write his name into the starting lineup in permanent marker. The appeal with Nik Stauskas is that he's an all-around offensive player who can shoot the lights out but also help to keep your offense working by making smart decisions with the ball. Guys with his shooting talent who can also chew gum and dribble a basketball at the same time are a valuable commodity in the NBA. Stauskas will continue to be an asset wither he's starting or coming off the bench because you always need roleplayers who can shoot. With Elfrid Payton, he really has to stick as your starting PG or you've basically wasted the pick. And it's also fair to question whether a team that's trying to put rebuilding behind them can afford to go into the season with an unproven rookie and a shaky sophomore as their starting backcourt (though Collison/McCallum/Payton sounds solid to me on paper).
So there's a lot of good reasons to take Stauskas over Payton, objectively speaking. Every time NBA analysts rate the draft they look only at obvious surface level criteria (what positions do they need) without considering all of these other factors. When you're picking 7th in the draft, it's wise to consider bolstering your depth at a given position rather than just looking to fill an immediate need because the talent level gets thinner as you move down the draft board. But at the end of the day, it's really just talent that wins. I see all the reasons for picking Stauskas and I don't hate the pick, but I believe Payton has got a good shot at being the best defender in the league at his position in 3 or 4 years and he's not a liability offensively either. All of the same criticisms people make about Elfrid Payton were made of Rajon Rondo before the draft as well and he turned out alright. If Payton is the better player long-term, it was the wrong pick. I think he will be, but we're a long way away from making that determination.
The draft day video thing though, I did cringe when I saw that video the first time. It sure looks like Vivek made the pick and it also looks like Pete wasn't completely comfortable with it. It was an awkward moment to expose to the world, but it's not a huge deal. We know Vivek is enthusiastic and involved, and I'm sure there were a lot of discussions that went on before this that weren't captured in the video. I suppose there's worse things that could happen with your team than a new owner coming in, getting a new arena built, and wanting to be a little too hands-on with player decisions. As long as he's willing to hold himself accountable for wins and losses along with everyone else, I don't really have a problem with it. By all accounts, Vivek is a pretty smart guy. I think he's smart enough to try a different approach if the moves he champions backfire.