Why keep his mouth shut? He should be able to speak his mind as long as he isn't breaking any rules. But he broke the rules, which is why he is getting the fines.
The NFL has determined (or at least are claiming) that there has been little or no spread within facilities, that people are getting infected and bringing it into the facilities but it isn't spreading there.
I don't know if that is actually true. But I don't think it is safe to assume that Cole Beasley is or has infected other players.