Keep your pants on Spartacus. Tilt at windmills and lose your income. Other people work to weaken the system by exploiting every weakness they can find in it.
Have you quit your job? Or have you been lucky enough not to be faced with it?
If you think this is a problem that can be solved with a fake vax ID, then you don't understand the scope of the problem.
(The problem, of course, is that your employer is assuming an authority that it simply doesn't have to demand proof of your participation in a "vaccination" approved by the FDA for emergency-use only. Whether the document you provide is legitimate or not, you have acquiesced to the demand that you comply with a very irrational request; you've given up the fight, even as you tell yourself you've won because you think you've found a "loophole".)
I'm expecting to face an ultimatum in the next several weeks; I've made my decision that this is the hill I will die on.