It's true that getting SSI or SSDI for just "anxiety" would be really difficult but Eric claimed to be diagnosed with bipolar disorder earlier this year. He could (in theory) also get it for PTSD (he does claim to have been raped or whatever)...
Also, either of them could've been on SSI since they were minors, which is often how it goes. You can get an SSI check if your child has an ADHD diagnosis for fuck's sake much less autism and actual serious problems. It wouldn't be difficult for them to continue getting it into adulthood, either. I'm not saying that I think that's what happened, just that it's not difficult especially in poor places where people know how to take advantage of the system. Generational welfare is a thing.
In any case, since Eric is married the SSA would count some of Rickie's income as Eric's, which would reduce what he gets in SSI (and possibly make it so he doesn't get anything, depending on other factors). As for Becky, she's not married to Amberlynn so as far as SSA is concerned Amberlynn means fuckall and her name is on NONE of those bills. Becky's name is. Anyone applying for assistance is not going to admit that someone else is paying their living expenses if they don't have to. It's a lot harder to explain it away when you're married, or living with family. But Amberlynn is just a "roommate."