Exactly.
And it's not unprecedented for teams to stick with a veteran who is safer than a rookie/unproven QB who looks better in practice. Not sure if this is revisionist history on his part, but I always remember Belichick saying in the Brady 6 documentary that Brady had a better training camp/preseason than Bledsoe in the 2001 season but what "stopped them from making that decision" (to bench Bledsoe for Brady) was Tom's inexperience." (Again, I find it hard to believe he would have benched Bledsoe without the Mo Lewis hit... but he did bench Kosar in Cleveland so who knows)
There were several sources that stated the same regarding the 2001 preseason. I recall reading the same in a book about Peyton Manning of all places.
Took a bit of digging, but found the following stats from the 2001 preseason:
Bledsoe: 36-63 (57.1%), 337 yards, 1 TD, 1 INT, 5.35 ypa
Brady: 31-54 (57.4%), 389 yards, 2 TD, 0 INT, 7.2 ypa
Huard: 13-18 (72.2%), 119 yards, 0 TD, 1 INT, 6.6 ypa
Bishop: 2-7 (28.5%), 21 yards, 0 TD, 0 INT, 3 ypa
Looking at the box scores, Brady got the majority of snaps in the first game, with Huard relieving him. Bledsoe got a series at the start, and Michael Bishop threw the final passes of his NFL career at the end. In Game 2, Brady and Bledsoe split the snaps, with Huard getting a handful late.
Bledsoe got most the snaps in Game 3 as the presumptive starter; interestingly, that was the one preseason game the Pats lost, getting dusted 20-3 by the Bucs. Bledsoe and Brady then split all the snaps in Game 4; it was unusual for starters to play the 4th preseason game, so not a good omen for Bledsoe.
It was clear from the usage that Brady was the clear #2. What would have happened if Bledsoe had not gotten hurt is unknowable, but certainly possible that he could have been benched had the team been losing and Bledsoe continuing to decline.