Linus' gifted-child problems aside, calling Linus out over a refusal to use "systematic version-control" might have had some small role in causing Linus to write Git, if for no other reason than spite. That alone makes this an amazing email.
I think it's unlikely: The 5-year gap between those two events seems a little long, and during that BitKeeper was used for a few years so it's not like alternatives hadn't worked.
It was more that Tridge "reversed"[1] the Bitkeeper protocol, leading to licensing issues and the eventual separation of Linux from Bitkeeper. The need for a high performance, distributed replacement motivated Linus to write a git.