Two points here:
1. You write "True, and that is what makes science a theory, it makes assumptions which cannot be determined to be true or false." This is not correct. Science strives to theory. Theory is the highest level of achievement in science (see the definitions I posted earlier). Any assumption, hypothesis, or theory which cannot be falsified is not really science.
2. You write "It assumes that because something is not falsifiable, it it false." Again, not correct. If it is not falsifiable, it is not science. (ID falls within this category: If I can't understand it, then a diety musta did it! Can't be falsified: not science.)
My bad. You are correct. It not necessarily false, it is just not science if it is not falsifiable.