Matthew, You are correct. That stuff that is falling apart is part of the original insulation. It resides behind the dash from left to right side and above the pedals. Given the age of our cars it is extremely common to see that falling down all the time on the floor. It is safe to remove. Many people opt on leaving it bare, or replacing with dynamat or other modern insulation if you want noise reduction. But it's not like it is really any noisier without it.