I know an ex-MLB player who said there were some players who actually never got it, though have the papers. In the US and other countries, certain states don't use or require anything to be uploaded to apps like here in Canada. So it's a lot easier down south and in other countries than Canada.
As well, I know someone in media who told me some Blue Jays players were hesitant and didn't want to get it though they eventually got their shots before the season started.
As for other sports, there were news stories about some NFL players who got caught using fake cards at the beginning so they wouldn't forfeit salaries, go for extra testing etc. I'm sure there were athletes from other sports as well. Not saying every athlete did, though I'm sure there are several athletes across many different professional sports who never actually got the shots. Athletes have the money as well to access that type of service.