The governor is carrying on an affair with a West Virginia employee using state facilities, state communications, and state time. But you think it's nobody's business but his own. Unbelievable.
Technically, you're correct. But the only thing that makes it public property is the fact that he used state facilities on the taxpayers' dime. If that's the extent of state involvement, then I think this is a dirty way to weaken your opponent.
On the other hand, did his little sweetie get any special favors, courtesy of the taxpayers? Did she get a raise or a promotion she didn't deserve, due to his influence? If any of that is the case, that is the sort of conduct that goes beyond having an affair.
I still think it's rather icky for the paper to publish this stuff, though. If we all know they had an affair, isn't that enough? Why do we have to get a blow-by-blow (so to speak) account of what they said and what they did? The only legitimate reason there was for all the gory details of Bill & Monica to be in the Starr Report was because Bill said something under oath that wasn't true.