The owner and/or manager of the restaurant should have learned the rules for properly displaying the flags of two nations in front of his business.
In the United States they are flown on two separate poles of equal height. The flag of the United States takes the position of honor, which is it's own right (which would be the viewer left). If only one pole is available, then only the United States flag should be flown. You never fly the flags of two nations together on the same pole, except in time of war as a sign of conquest. Otherwise it is considered an insult.
The vet in question (assuming he is a real vet and not a publicity hound) should have asked to speak to the manager of the restaurant, and politely informed him that his business was effectively insulting the flag of the United States. Then simply asked him to remove the Mexican flag at least until he had another pole to fly it from separately.
He should not have vandalized another person's property but cutting the flag down instead of lowering it and removing the flags. And he should not have walked off with a US flag he did not own.
The TV station itself should have explained the situation to the restaurant, instead of camping out and waiting for a hot head to create good video for TV.
A textbook example of how NOT to resolve a situation.
FYI, the below picture shows an appropriate time to display the flags of two nations on a single pole:
Captain Daniel V. Gallery, on the conning tower of the Kriegsmarine submarine U-505 shortly after her capture by US Navy Task Group 22.5 on June 4th, 1944.