their privilege to own property which was, in the final analysis, stolen from the ethnic and cultural ancestors of one of the parties

The guy on video has no stolen property rights. Ancestors privileges and losses are not transferable.

There is the primary focus of immigrants as a "burden" as if they cross the border, sit on their ass, and start sucking down welfare checks

It is not depend on immigrants, it depend on state. In social state, yes, illegal immigrants consume from public funds more than they send to public funds:

http://www.cis.org/High-Cost-of-Cheap-Labor#taxrevenue

Ignored is the fact that Immigrants do work

If a person earns 30K and his family consumes 40K in education and medicine it's a burden, not profit for a society.

The "illegal immigrants as economic burden" construction is just another of those pre-packaged talking points

It is simple: if illegal immigration is a profit for a country then different countries would compete for illegal immigrants. But they don't.