If they are in some way dodging contracted benefits like severance, are in any way defaming the employee, or are trying to prevent unemployment claims, it is going to be illegal to invent cause. People really misunderstand "at will" and think it means that an employer can fire you for any reason at all. It doesn't. It means they can fire you for no reason at all. They cannot fire you for a protected, illegal, or fake reason, and they still are going to have to honor your contract, make good on the unemployment, et cetera.
There really isn't any difference between a "no cause"/at will termination and a layoff. Maybe some fine technical points, but for the layman it's the same thing.
And in many states what a previous employer can say to a future employer as part of a reference check is limited -- in Cali, for example, any "malicious" statements can get you in a lot of trouble. If you suspect a previous employer might be doing this, talk to a labor lawyer.
Recording and trying to go viral with these exit interviews is the wrong response if you feel you are being wronged. Sure, record it (if it is legal to do so), but definitely do not upload anything until you have talked to a labor attorney.