I totally understand the (perceived) risk and concern and I don't say this with nieave perspective , but in general terms I think there's some sort of natural order / equilibrium where people just get on with it and don't reveal. Ok, big mega stars probably have to watch out but even these days CEOs, civil servants, academics, health professionals may have a media presence not just showbiz and we know there's bound to be a whole bunch of that cross section who are at it, but things seem to tick over.
I think it's different if aforesaid CEO is uncovered for financial scandal or a high profile affair then the media throws in the other "lurid" details. Maybe, the resosn for why someone makes the papers could play a role in whether the press will pursue the prossie angle?