Is Kato a stereotype in the new Green Hornet movie?

As I was watching the Simpsons, during the commercial, there was a funny little ad that had the two actors (all dressed in their outfits) at a fast food restaurant drive thru, and as I was watching that ad, I can't stop thinking about the doentary that I saw on the history channel about Bruce Lee. In the doentary, they talked about this one incident during the set of the Green Hornet TV series where Bruce was talking to an actress and someone came up to him and said to him "Boy pick up so and so", and Bruce Lee is like "excuse me?" The actress was like "you know who this is?" But the person didn't care and was apathetic. The actress asked Bruce if that bothered him, and Bruce Lee told her "if that bothered me, I wouldn't be Bruce Lee." I don't know why I was thinking about that doentary and I understand Bruce Lee was dressed in his Kato outfit, so that was an honest mistake, but what's interesting is even after so many years, I still don't understand why asian male actors in the U.S. today are limited to just asian roles. Bruce Lee has influenced so many.