Of course you can refuse. But the right to refuse is not granted by HIPAA either.
OK, so people can lie. Can employers demand that health care providers confirm the data?
There is no real way for anyone to check whether you have actually been vaccinated.
There isn’t any federal database. Thankfully, Ron Paul helped pass a bill to block those back in 1998. Piglosi tried to remove this restriction in 2020, but it died in the Senate.
Virtually every State database has an opt out provision. You just send a notarized letter asking to be opted out of the state database, and they are required to delete everything about you that might be in the database. Thus, once you are deleted, there wouldn’t be any State record regarding your vaccinations.
Accordingly, beyond that paper card, there isn’t any “proof” that someone has been vaccinated.
The cards are very easy for anyone to print that wants one.
Lot numbers and dates are all over the internet because of the Karen virtue signalers.
The card stock is available at Staples.
The blank cards are on various government websites.