As far as civil (constitutional) rights go, it would appear that the facility is private so there are no constitutional rights implicated. Whether there are stautory rights that are violated, I doubt it. As a practical matter do you really want to go to the expense of a civil suit over a TV?
You did a great job of laying out your issues--something eight tenths of question askers fail to do--well done.
My sense is that the federal government did NOT intend that facilities would have to make arrangemetnts for patients to bring in their own personal large screen TV's into a facility.
Likely, your rights regarding a flat panel TV will turn on the Rehab Center's rules and regulations. Recommend you review those relevant documents for initial guidance. Even if you find no specific prohibition against the TV you brought, I can foresee the facility still prohibiting the TV on grounds that (1) its an issue of first impression and they hadn't noodled through all the issues (2)rights of others, (3) insurance issues and (4) although a stretch, perhaps safety too.
Best option is to negotiate with the facility Administrator on a one-on-one basis.
I wish you a speedy recovery whether its in front of a 20" or a 32".
NOT LEGAL ADVICE. FOR EDUCATION AND INFORMATION ONLY. DO NOT RELY ON ANY ADVICE YOU RECEIVE FROM ME OR ANY OTHER ATTORNEY IN THIS FORUM. Legal advice comes after a complete review of the facts and relevant documents and an expressed (written) agreement of representation that forms attorney-client confidentiality. Neither of these two events can occur in this forum. Mr. Rafter is licensed to practice in the Commonwealth of Virginia and the US Federal Courts in Virginia. His answers to any Avvo question are rooted in general legal principles--NOT your specific state laws. There is no implied or actual attorney-client relationship arising from this education exchange. You should speak with an attorney licensed in your state, to whom you have provided all the facts before you take steps that may impact your legal rights. Mr. Rafter is under no obligation to answer subsequent emails or phone calls related to this or any other matter.
If I understand correctly you are asking whether you can sue because you are being permitted to watch a 20-inch TV but prohibited from watching your 32-inch TV?
If so, I see no basis for a lawsuit. You have no damages from being denied access to a larger-screen TV. You have no 1st amendment or other constitutional right to watch TV on a screen size that you prefer.
Just a guess, but I assume the Medicare guidelines that you found online apply to long-term facilities, not short-term rehab.