Philip, he's not giving a sworn deposition here. It's one sentence from a much longer interview on a podcast without considering its context. To me, it's clickbait - and not something that would have any legal repercussions whatsoever.
MLB teams are not allowed to announce positive tests of players for legal (HIPAA) reasons.
They do announce when they put guys on the Covid disabled list, as the Phillies did yesterday with 4 guys including Tommy Hunter. Technically that is not proof the guys tested positive because you can go on the C-19 list if you are positive, if you have symptoms and are awaiting testing/test results, or if you have been exposed to someone who has it.
You could also find out if a player has it if he announces it himself on social media or whatever.
But the team can't come out and say it.