Check your facts before saying I’m not right (and see post #30). Spaniards are much paler than these guys; they are American Indian who happen to speak Spanish, like our full-blooded Indians speak English. However, I agree that if they had to prove NO European blood whatsoever, that would be hard to do.
Spaniards are often blond or red haired and blue eyed (not always). Since they pretty much run the place, there is a kind of color hierarchy there as well as there is in the Caribbean (and Asia, truth be told).
Original people are either same as American Indians or, much less common, strikingly distinct from them or from either of the others. The Apache in our movies were largely from Mexico, further, the border splits many 'natural' tribal boundaries between the two countries - that's a real problem with stopping ALL cross border traffic (see To'hono Odam etc). Think of the many variants on 'American Indian' that suggest Bering bridge origins versus all those pre-Colombian statues at the museum.
By far most Mexicans are Mestizo, European (Spanish) and Indian mix; hence the raised hackles over calling themselves 'La Raza'. The 'average Mexican' isn't in charge of a whole lot within Mexico and most of 'our' illegals come from that class.
Like every other place in the world, just about everyone there was an invader at one time or another but in Mexico it's hard to find the 'absence of European blood'. (PS: LONG time ago I had an interest in Arizona indians, the locals imported dancers etc. from Mexico for their festivals - saying it was a form of charity for lower class indians south of the border; class consciousness isn't limited to any particular group)