Wrong. It's an at will state, meaning you can fire someone for any reason whatsoever. The only way you can run afoul would be to get in trouble with the feds via the equal opportunity route, and last time I checked that was limited to a select few criteria such as race.
I assume you are referring to "right to work" states?
The pro-korporate HR and lawyer types have done a great job in convincing people that "right to work" equates to "we can fire you at any time for any reason".
This is simply wrong, and an attempt to 1) scare employees into compliance, and 2) reduce the number of lawsuits against them.
All "right to work" says is that companies can't fire you for not paying fees to the union. And that companies CAN NOT include union security clauses in their collective bargaining agreements.
"Right to work" is, in a fact, a restriction on what companies can do on their "private property", yet some folks here have contorted into something totally different.