That's one of those Pandora's Box thingys. Not quite sure at what point (almost) everything became fair game for the mainstream media, although I'll blame the influence of National Enquirer-type fishwrappers and TV shows. And no, I doubt most anyone here would enjoy the fishbowl treatment accorded to celebrities these days.
Most of the fans I knew back then had heard and discussed the stories about Kelly's crew, though. (I should note that the tidbit about Thurman sleeping it off in the trainer's room, so he wouldn't be late for practice the next day, came directly from him.)
Should we sit in moral judgment of people we don't know, based solely on what we read/hear? Perhaps not ... but we do, don't we?
Here's a question to ponder: what would have happened if the guys covering Mickey Mantle had written about his nights on the town? (Now THERE was a guy with "quite the alcohol problem.") Would he have denied it, or sought help? And would the adversarial relationship between the media and the teams they cover (generalizing here) have existed much sooner than it did?