The ones I'm talkiing about have no problem plopping down $250,000-$800,000 CASH MONEY for a house. Do you know what kind of house that will buy you in Texas?

They are essentially buying a vacation home in Texas. No one gives a rat's hiney where you're from when you're paying CASH for a house. As far as leasing, the leasing agents are happy to lease to them in this market. Very often, they pay a few to several months' rent ahead of time and the agent loves that.
As for jobs, they don't get jobs. Their money comes from Mexico. The dad flies down as often as needed to conduct business. Wife and kids stay here.
Keep in mind, I am talking about the wealthy Mexicans, not the illegal aliens we used to see. Two different groups of people, two different sets of rules.
As far as being illegal, I don't know that they are. There used to be something called the million dollar visa, which I think has been downgraded to the $100,000 visa.

Something about investing $X in a US business and you get a visa. Many are doing that. But the vast majority are coming here on tourist visas, staying as long as that allows, returning to Mexico to get a new tourist visa, coming back to the US, rinse, repeat, rinse, repeat. Sure, sometimes the kids have to go AWOL from school for a while so that they can return to Mexico to get a new tourist visa, but so what???? Money talks. No one bats an eye at a wealthy Mexican wanting multiple tourist Visas to the US.