I have seen many many styles of Mexican cooking and none of it resembled what was in the video. What was in the video looked like some thing thought up by some Gringo on a Chef competition show. There is no respect paid to the food or the culture.It's a San Luis Potosi thing. Different regions of Mexico have different styles of cooking.
I have been with friends hunting in deep south Texas and the food was cooked on a recycled disc from a disc harrow.(A type of soil breaking tool)
It all looked like what you see in Mexican restaurants.
As far as that goes a lot of the food served from fast food places is not right either.
Most of the meat served is from roast or steaks cuts. Barbarcoa de Cabeza is tasty if you can get past what you are eating. It is an entire beef head cooked in a earth pit with a wood fire, Mesquite usually. It is a pit literally dug into the ground and the food is covered and placed on the coals then the earth is piled back on.
Lingua(Tongue) is still one of my favorites. I cook it here from time to time when time permits.
When cooked properly it has more good flavor than any other part of cattle. It use to be delicacy in America before the 1930's.