If you're desperate enough, sabotaging yourself to qualify for a need-based social program eventually becomes the objectively optimal thing to do. This is the first I've heard of that sabotage extended all the way to intentionally getting AIDS and intentionally not seeking treatment, though.
Typically these stories can be dismissed for the anecdotes they are. I have a handful of right-winger friends who love sending me some article from the Wichita Star or something where some woman got promoted at her job, lost her Medicaid benefits, so she quit her job, and now gets even more benefits, or something, and RAAAR $16 TRILLION IN DEBT WE'RE ON THE ROAD TO GREECE MAKERS TAKERS SMALL BUSINESS THIS COUNTRY IS GOING TO HELL.
No, this country has decided it's beyond the state's responsibility to provide food, shelter, and medicine to everyone. Instead, various state and local programs only provide it those things to a fraction of the people who need it, usually based on some seemingly well-intentioned criteria. And then some people have the kind of lives where being a homeless prostitute without AIDS is worse than having a roof and having AIDS, so they decide to do that.
You can accept that any program like this will induce morally hazardous behavior in some people, and look for objective information vs. sensationalized anecdotes to see if that program needs reform. You can also realize any need-based program will almost always introduce said morally hazardous behavior, and the problem is that we underfund these programs so that they need this need-based criteria to begin with.
Or you can push to eliminate all these programs because you think they turn everyone into lazy welfare AIDS-seeking moochers, and the good news for you is there's already a political party in the US that pretty much supports all that.