In the NFL, all injuries/illnesses have to be reported to the league, and are made public. You could check the injury report for all 32 teams right now, and they have whether a player is out, doubtful, questionable, or likely. A team gets in trouble if they don 't report an injury. Also, there is drug testing, and the info is released.
And more detailed information is released. If a baseball player is going to have Tommy John surgery, everyone knows it. If a player is having ACL or UCL surgery, everyone knows it, and how it is progressing.
On the Monday Night Football game where Hamlin was out, there was real time news and speculation on what was happenings. I remember watching and thinking he might be dead. The announcers were updating info as it came out. So, the public knew about his condition, before he did, because he was not conscious.
I have seen surgeons give press conferences after they operate on a player. (Obviously it has been signed off.) It's reported if they have the flu or something like that. About a month ago, they even reported a QB's flu was worsened overnight.
Aaron Rodgers was asked about his vaccination, and he gave an answer that may have been technically correct, but was perceived as implying he was vaccinated. When it came out he wasn't vaccinated, he's still being criticized for it. Aaron Judge, a player on the Yankees, refused to answer whether he was vaccinated, and the media said this meant he wasn't vaccinated. (Whether he was then or not, he was later because he played in Toronto.)
So, it's pretty unbelievable that he wouldn't think he was going to be asked that, unless Michael Strahan had agreed not to ask that, but in that case, I think it would have been a huge controversy. I don't know what caused his cardiac arrest, but if you watch the clip, it's something he is deeply afraid of revealing.
I recall watching the NFL draft one year. I don’t recall the question but the player stopped his answer, saying “oh, you told me not to say that.”