I don't like the media building people up as heroes. Too often, they do that just to knock them back down when the wind changes and it looks like that approach might sell more advertising space.
Sadly, there are police officers, ambulance crew, nurses, fire officers, social workers, teachers and other public servants who are injured, suffer long term mental or physical health problems or are even killed while carrying out their jobs of trying to ensure the health, safety and welfare of other people. In that respect, they are ALL heroes, whether the papers report it or not.
I think the OP's point is that some behaviours and actions may "take the shine" off a hero in the media, make them less likely to be lauded in the press, particularly if crime or something seen as "immoral" is in their background. However, domestic violence doesn't seem to be a big deal. Look at Frank Sinatra, George C. Scott, John Lennon, Sean Connery, James Brown, Stan Collymore, Paul Gascoigne, Phil Tufnell, Chris Brown, etc. All were violent towards their partners. All retained significant support from fans and the media after the beating their partners. It just didn't register as being that important.