> Wikipedia makes me believe that Mexicans are generally a mix of European and native ancestry.

The interesting aspect of the article is that the "native ancestry" part is very diverse itself.

> But why does Mexico have so much more of that than the US?

The Spanish mixed with the native population and created communities with them since the beginning. This process is 500 years old. Race boundaries have been erased. In the US this process is 100-200 years old.

> Especially considering we stole much of our land from them...

A lot of the land was very sparsely populated. Most migration to the West occurred after the 1840s. People coming from the East (NY, Boston, Philadelphia, Louisiana, etc). This explains why they are so similar to them.