A strawman argument is when you restate someone's argument in a way that's stupid, then you refute the stupid argument. Or in the extreme case, argue against an argument that the person never made. In both cases, you're not arguing against the other person, you're arguing against a straw man that you made up. Hence the name.
It's still a logical fallacy, just a different one. Fallacy of relative privation applies.
https://en.wikipedia.org/wiki/List_of_fallacies#Fallacy_of_r...
https://socratic.org/questions/what-is-the-difference-betwee...
(Similarly, a weakman is when you seek out someone who genuinely holds a weak (easier to argue against) version of the position you wish to push against, argue against this weak version, and act as if you have argued against the stronger versions.
Neither of these appear to be what has been done here.
Saying "we have to fix state prisons too!" is not an argument against "private prisons are a moral hazard". We should do both!