After a bit of quick thinking, it seems to all work out ok. As long as you assume that nothing in time can be ever changed, aka it was all destined to happen.
Because, if I remember BttF3 correctly, Fox would've never existed unless he had gone back in time and saved his grandfather. Which couldn't have happened unless time travel was inevitable. I could be remembering the movie wrong, it's been a long time.
Then this also means that the change in Fox's family in BttF2, when Biffs becomes their lackey, is a destined discontinuity in Fox's timeline. Weird.
Doc must've been lying, or simply wrong, about the future being unwritten. Otherwise anytime you traveled in time, that timeline moves forward without you in it, and thus you would never see your own future. And thus the movie wouldn't work. We can't have that now, can we?
dfi