I don't know. Bob loves to throw people under the bus. I think Bill was facing a double edge sword. He was brought in to get the team back to the playoffs as they still had enough core players, but were on the verge of 3 straight years out of the playoffs.
I'll preface by saying Drew Bledsoe was my favorite QB growing up when I was a teenager. I loved his unorthodox throwing mechanics and could fling the ball 50+ yards with ease. In 1999, I blamed the rest of the team for not having an OL, RB, aging TE, lack of 2nd option at WR and a poor defense. By 2000, something just didn't look right with Drew and it continued in 2001 when he was on the verge of being 0-2. As much as I was a big fan of Bledsoe, they would've struggled just to get to .500 with him in 2001 and that's where I think Bill would've been fired. With Tom, they were 3-4 against teams .500 and above that season. That record would've been even worse with Drew. In fact, the worst team Tom lost to was a 8-8 Broncos team. Drew lost his first game of the season to an eventual 6-10 Bengals team. He was a high maintenance QB that didn't do well when the talent wasn't surrounding him. Tom took what the defense gave him.