"So Friedman's argument is actually the opposite, "let's reduce welfare so we can afford to have more immigrants here!""

No, this is YOUR interpretation of this statement. First, the statement is neutral. Knowing Friedmans background it is clear that he was not a big fan of a welfare state (yet the idea of basic income is from him).

"..we can afford to have more immigrants here!" No, the immigrants I was talking about would just not come anymore.