True, untrue? It doesn't really matter. The issue facing Palin and her brand of right wing fundamentalism isn't what happened but what people are prepared to believe happened. Just as Tina Fey's parody of Palin -- "I can see Russia from my house" -- came to be viewed as an authentic Palin statement despite incontrovertible evidence that Palin never said any such thing, the image of the entire Palin family involved in a drunken redneck brawl doesn't need to be true to damage her any anyone associated with her politically.
Even if there was no brawl, that seems pitch-perfect-Palin enough that the image is impossible to dodge. It's part of Palin's baggage now and anyone who wants to stand on her Tea Party shoulders is going to have to cope with it too.
The same sort of thing holds on the left too, of course. For the folks who viewed Obama as a secret muslim or held to any other Donald Trump endorsed conspiracy theories, the reality didn't matter; the idea of Obama as "other" enough to be a Muslim or a Kenyan or anything else felt accurate enough that they were willing to accept the accusation without or even in spite of evidence.
This is image politics at its most powerful. The difference is that, unlike Obama, Palin and the rest of the Tea Party bring these attacks on themselves.