You know, I had never thought about this aspect of the first movie too much before, but you're right, if you look at this too closely it does all unravel. Even more so than it already did that is. But it's still no worse than Back to the Future 2 where Doc says they can't travel back to the future to stop old Biff from stealing the time machine because history changed. Except old Biff already did exactly that which is how they had the time machine at that point in the movie anyway.

Really though, this is not a series that was ever supposed to be examined in too much detail when it comes to the time travel logic behind it.