Can an employer terminate you for other reasons not stated in the letter?

Under Federal Law you are an at will employee and the employer can terminate you for reasons not stated in the separation letter. However, if the reasons articulated in the letter materially differ from the reason for the ouster, than it may be indicative of a pretext firing for a prohibited reason and may be actionable.

An employer isn't required to give reasons at all. they can just fire you if they don't like your shoes, so long as you're an at will employee. However, a covered employer CANNOT fire you for a prohibited reason (for example, your race/sex/disability.) If you believe that the secret reason is discriminatory, you should immediately speak to a local employment attorney.