He was awarded the Silver Star four times. He was never awarded the Navy Cross, and was never nominated for the Medal of Honor. Audie Murphy received his Medal of Honor before he made the movie, not the other way around.
It is not the movie that is earning Kyle calls for recognition in belated honor, but that the movie brought to the attention of a country the actions of a quiet hero who chose a hard road in the military (a SEAL a decade older than his compatriots), went to Iraq 4 times while most of us spent that decade time playing with our kids, shopping and bitching about taxes, and went out with the troops to search and destroy bad guys when sniping didn’t seem like enough action to save the lives of the troops on the ground.
The movie did not make Chris Kyle. Chris Kyle’s life made the movie