If they let you go and state no reason, then it would be up to you to PROVE that the reason (if any) they had was unlawful. That's pretty damn close to carte blanche, bucko. If they keep their traps shut and don't document in writing anything about such unlawful reasons (such as age, sex, race discrimination), then the worker and the worker's attorney are pretty much stuck like Chuck.
In theory, you are correct.
Speaking from the management side of the desk, I wish it were that easy.
Fact is, most companies' internal policies require documentation (no exceptions) before an employee is terminated (for any reason). I have never worked for any company (big or small) that would allow someone to be dismissed with no documentation at all.
Some small employers do not have such policies, but most of these are not aware/sophisticated enough not to leave some sort of trail.
Theory vs reality.