Bioshock 2 suffered greatly because it tried to follow up Bioshock directly, despite the fact that the first game neither needed, nor really left any opening for a sequel. This, in my opinion, would have been the case even if it had been Irrational that had worked on it.
After I saw my first trailer for Infinite, I immediately started ignoring all press on it, reason being that I thought it looked so intriguing, and didn't want to put myself in a position where I'd seen and heard large chunks of what the game had to offer before it was released. As a result, though, I have no idea why this game still wears the Bioshock label. I don't how it ties to the whole Raputre/Andrew Ryan/Jack/Big Daddy/Little Sister/Adam deal.
That said, I'll be buying it almost immediately for three reasons:
1.) Ken Levine had a hand in it, and anything that man touches deserve consideration.
2.) It wears the Bioshock name, and the first game is easily in my top 5 list.
3.) It isn't trying to be a direct sequel, so I'm interested to see how it ties into the first game. And the second one, I suppose.
Hell, if the game is strong enough on its own merits, it doesn't even need to tie in to the first game. I'd be confused as to why it bears the name Bioshock, but it wouldn't be a deal-breaker for me.