Actually, states can, and do, kind of mess with SSDI. The first decision to grant SSDI - or not - is made by the local Disability Determination Service, which IS a state agency. They are contracted by the Federal Govt. (by the SSA) to provide that service and make that judgement. When I was applying for SSDI, my doctor warned me that the state where I lived was much harder to convince of disability than, say, California. As I think you know, there are web sites listing the relative leniency - or lack thereof - of various states. I guess something comparable is going on with HUD.

I don't think that the state's taxing authority has too much to do with either of these benefits (Social Security, or Section 8 subsidy.) Each state knows that it has many more citizens wanting a benefit than there are dollars to go around to provide them all with the benefit. So the state's interest, I would suspect, is in trying to make sure that the benefit goes to those most appropriate to get the benefit. (The state has no reason to turn down any Federal dollars. It does have good reasons to want to influence who, among its citizens, will be the ones to get those dollars.)

My understanding is that none of the 50 states are trying to tax the Pension for Aid and Attendance. Here is a link to support that:
Is the aid & attendance pension taxable?