Sam is right, Chris was fine with it - in fact Chris TOLD him walk behind him like he did. I know what you thought you saw, but that's a huge green and he was pretty far behind him - much more than 10 feet.
Also, remember at the time Phil was "the best golfer to never win a major", so when he won, it was a huge deal for him and his family. Consequently, his remark to his kid was justified.