Recognizing a stereotype isn't racist. They are known to us all, even if we don't believe them. There are some I know only because other people have said them that I'd never have known otherwise.
No it isn't, he's acknowledging a well-known racial stereotype and connecting the dots. Doesn't make OP a racist.
Guess calling him an outright racist is a bit much, but it certainly speaks to how he views the world. Personally the thought hadn't even crossed my mind until I read his post.