It is indeed possible and likely will happen; however, even the CDC says that if you are vaccinated, it is safe to be around those that are unvaccinated, even indoors and even if they are unmasked.
So ultimately, those that lie about it are hurting themselves (if masks actually do anything and considering that even Fauci has recently said they are just a placebo and do nothing) and asking for proof will only line the pockets of people that will create fake proof. In fact requiring proof may result in more people refusing to get vaccinated in the long run because many will feel like they are being forced and the people that would creat fake proof would become very accessible, especially near anywhere requiring proof.
Don't believe me? Look at medical marijuana, before it was legalized for recreational use, you could go to almost any street corner and get a card for $20, I know because there were blatant holding signs up, apparently you didn't even need to get out of your car.
Or back when Disney used to require doctor's notes to get guest assistance for the disabled, they were available for about $5 on many street corners.
This would be no different, although the dollar amount might change.
