i've never been comfortable with the usage of the term "outing gay men" in this specific fairly negative context.
their fallacy isn't being gay -- that by itself is nothing wrong and should never be associated with a public shaming exercise.
no, the problem in this scenario is their hypocrisy in denigrating other gay men for their activities while indulging in those activities themselves.
this whole series of events should be called "exposing the hypocrisy of loud-mouths" instead of "outing gay men".