True, but there are also various laws in the different states that determine whether contracts can even cover this point at all. California, I believe, has laws in place that override employee contract clauses that claim ownership of off-the-clock employee inventions.
So, if the OP was in California, his employer really had no leg to stand on, regardless of what he may have signed when he started the job.
You're mistaken. The California statute makes an exception for work that relates to the business of the employer. I quote from the addendum to the offer letter I received for my current job:
In compliance with prevailing provisions of relevant state statutes, this agreement does not apply to an invention for which no equipment, supplies, facility, or trade secret information of the employer was used and which was developed entirely on the employee's own time, unless (a) the invention relates (i) to the business of the employer, or (ii) to the employer's actual or demonstrably anticipated research or development, or (b) the invention results from any work performed by the employee for the employer.
That language is probably straight from the statute, though I didn't check. Anyway, it would have to be written this way, or it would be an invitation to rampant abuse by employees. As it is I think it's very fair. Note especially the word "demonstrably".
So, if the OP was in California, his employer really had no leg to stand on, regardless of what he may have signed when he started the job.