I don't recall what they covered in Pirates (pretty sure the bulldozer race is in there), but BG definitely has a reputation for liking fast cars. In fact, Gates and Paul Allen lobbied to get changes to US auto regulations passed so that they could import Porsche 959s.
Nah, I have a particularly good memory for movie scenes. The construction vehicles scene and arrest scene are two different things. Bill gets arrested while speeding (while singing Sinatra's My Way in a sports car) and he wreck Paul Allen's car in the different bulldozer scene. Of course this is a movie so both can be pure fiction.