If the policy is NOT written in the employee handbook, (which I am sure you had to sign a statement acknowledging that you have read the handbook and that you are expected to follow its guidelines), my un-lawyerly opinion is that a sign posted on the bulletin board does not hold any authority. Any changes to the employee handbook should be made in writing and handed to each employee, and the employee signs another statement acknowledging they have been informed of the new rule/guideline/etc.
Otherwise, there is no way your employer could lawfully claim that 'all employees were made aware of the changes to the handbook'.
And +1 to researching further exactly what laws your state has regarding 'at-will'. In my state, which is 'at-will employment', its one way or the other, but not both. I can be terminated for no reason, I can quit for no reason. But the moment the employer gives up a reason, they can't hide behind 'at-will', they must be able to provide adequate documentation that there was cause for termination, or they risk facing a lawsuit.