"But he also urged adoption of a "negative income tax" in which people who earn less than a certain amount would get money from the government. "
That is just repackaged Marxist wealth redistribution. I wonder why he advocated that. We have it now as the earned income credit.
It was his suggested solution to alleviate poverty, as a replacement for the host of then-existing welfare programs (not in addition to).
IIRC, Friedman only advocated any kind of NIT as part of a comprehensive reform that would have drastically reduced overall taxes, moved to sales taxes rather than income, etc. If "they" took one PART of his ideas-that-were-meant-to-be-implemented-comprehensively, and ignored the other parts, one cannot blame Friedman.