They wont just keep stamping the same card endlessly until it is completely covered. How else is he going to accomplish this absurd undertaking but to have access to a bunch of official vaccination documents?
It's not outside the realm of possibility that he was also selling them, but I feel like Occam and Hanlon both agree that unless there is direct evidence, he's probably not some criminal mastermind getting rich. He's just a random person with either a fetish or something to prove.