My dad is undocumented. Can he fly within the US?

I called his immigration lawyer to ask her if he can take the plane traveling within US and she said it's not a problem. What do you all think? He has a passport from Honduras with no visa stamp in the back. He also has drivers license from his state, but the drivers license says "not for federal use."  Can he use any of these? The lawyer says it's fine and there shouldn't be an issue but I'm just seeking opinions. I find it risky for some reason... Or am I overreacting? I know TSA's job is to only make sure that our photo ID has matching name with the boarding pass and they also make sure we don't bring anything that we're not suppose to on aircraft. However, I am afraid that they'll question him about his immigrant status if they feel like checking the back of his passport. If the lawyer says is OK, should we take her word for it or not risk it?