Everything you say is true. You can also trace this form of psychological warfare back to WWII. Propaganda got a real bad rap because of how it was used to manipulate people around the world. It was repackaged and renamed as public relations.
This should have been the tipping point of governments rejecting propaganda and protecting their citizens from its effects. Instead they decided to use the best of psychology and sociology to continue to manipulate people. This is a basic violation of human rights so egregious that any government that allows it has betrayed its own people.
I appreciate your interest and research in this matter. When it comes to disability this determination is done at the Federal level through social security. This is how people get disability cash payments which is what most people think of when they say they get "disability".
While you are correct that individual states may have different means testing for SNAP, Medicaid, APA, etc. all cash benefits are mostly tied to this disability determination. Generally all states have strict income and resources limitations and in the case of TANF/SNAP also have work requirements. TANF is also limited to 60 months total in your lifetime.
All this money is usually from Federal sources although states will often be require to match funds. This is also why the rules are very similar since they are often dictated by the Federal government.
There really is no misunderstanding as you yourself admit it happened long ago and the details are murky at best. This is what I would call family mythology and helps to inform your world view. I was just pointing out that there are some inconsistency with this view.