Anyone who would try to discredit Chuck Norris and his real martial arts accomplishments is just plain ignorant to the facts.
Your actor in a martial arts films line may have some credit in modern films but not in films made back in the 70s and early 80s.
Most martial arts films were period films that featured particular disciplines or styles. The stars of these films had to be proficient in these particular styles (Judo, Korean Karate, Northern Mantis, Wu Shu, etc). Since most of these movies were made in Hong Kong and using proficient Martial Artists, these fighters came from some of the most prominent schools that existed. These schools had control over who could and could not make a movie that featured their particular discipline.
Any one who is knowledgeable about their own discipline or others can recognize when the fighter in the movie is using his or a particular style. Most of the fight scenes or training sequences in the movies back then were either a strict following of ancient forms or variations on them.
This added fuel to the fire that martial arts traditionalists had against what Bruce Lee did, because he would not and did not promote any particular style (in his movies he just called it Chinese boxing). He was willing to teach outsiders, he was willing to bend the rules of tradition and not go to the grandmasters and ask for permission to use their particular style.
This might sound like fairy tales but martial arts was banned in China as new people came into power. Much like gun control in modern times, the dictators did not want the common people to be able to defend themselves, making them reliant on the army or government for protection. Also it made keeping the people under their control a lot easier if they did not know how to use a sword or fight.
That is when schools went underground and monks and traveling theater groups became the way to save and practice the ancient arts. People like Jackie Chan who has demonstated many different disciplines over the years is not a student of any of the major martial arts schools of China but a student of the Pei King Opera company. The artists or actors in the opera company were allowed to perform martial arts under the disguise of dance or an acting performance skill.
It was not until modern times when Hong Kong was liberated or occupied by new rulers that schools were able to come out of hiding and teach openly. You might be able to understand why some would resist outsiders learning your style and people blending and corrupting what some wanted to keep pure when you and 10 generations of your family sacrificed life and limb to preserve the styles.
When you talk Bruce Lee, Chuck Norris, Benny Urquadez, Jet Li, Jackie Chan (the list is even longer) you are talking about real martial artists not Keanue Reeves studying for six months and using special effects.
I have all the respect in the world for this new breed of MMA fighters and the like, but know your history. It is good advice in any avenue of life.