What you are saying is technically true, but take this one case I have more personally experience with than I wish was necessary.
FPL for an individual is 12,060.00
FPL Chart 2018 - Federal Poverty Level 2018 - See Where You Stand
We have an uncle on my wife's side who is old, basically deaf, and effectively not ambulatory. He's in a nursing home that costs about 4K/mo. The nursing home won't let him use an electric wheelchair we bough him - mentally incompetent - runs into people and things. He can't manage his own finances or medications. He can't move a manual wheelchair because both of his rotator cuffs are torn. 12,061.00/year would lift him out of technical poverty (a statistic), but it would not provide for the care he needs. That's one reason I called that statement a "hand-wave". It pretends that a check/voucher to bring everyone "out of poverty" will solve the problems associated with ending all of the so called safety net programs.
I have a lot of problems with Medicare/Medicaid and would like to find a good fix for them. I think doing that requires us to address the fact that they cost too much, mostly because a) medical care costs too much, and b) much of it is eaten by the elderly and chronically ill.
JMO, and I haven't read that whole site so I might be missing something that guy is proposing.