Zeuxis goes first, and paints such realistic grapes that birds fly from the sky and try to eat them. Pleased with this result, he then smugly demands that Parrhasius draw back the curtain in front of his own painting. As it turns out, the curtain is the painting, and Zeuxis himself, like the birds, has been fooled. Parrhasius therefore wins, as fooling a human trumps fooling birds. Interestingly, according to the Washington Post: "Thanks to [Kippenberger's] troublemaking persona, some have suggested that he would have liked the way that the cleaning woman 'completed' his sculpture" - although this does seem to refer to a commenter called "fearslayer88", so I'm not sure how much store to set by that. One might think, however, that, much like Zeuxis and Parrhasius, Kippenberger intended for his artwork to look as lifelike as possible, and that this mistake is a tribute to his artistic skill, even if his artistic intentions were different (i.e. his realism was not to do with proving how well he could recreate the real world as an end in itself, but rather as a means of delivering an artistic message (I would imagine)).
That all assumes, of course, that this was a mistake, which leads me to the second Classical anecdote this story reminds me of. It relates to the notion of destroying art – and, somewhat indirectly, to the fact that the poor lady is, quite rightly, not named anywhere as far as I can tell. That was hoped to be the fate of the infamous (pun intended?) Herostratus, who intentionally set fire to the beautiful Temple of Artemis at Ephesus, one of the Seven Wonder of the Ancient World, for the simple purpose of gaining fame for doing so. The sentence was apt: as well as execution, that his name should never be referred to again by any historian.
There's a useful and fairly extensive list of sources for this story from the excellent Michael Gilleland (Laudator Temporis Acti) here, which might help you decide whether or not the cheeky arsonist won out in the end – certainly, his name has not been lost to posterity as was the hope, though he is hardly a household name. Does that count as immortal fame?
Now, is it likely that this cleaning woman didn't realise that she shouldn't clean the art installation? Did she clean any others? Or could it be that this German cleaning lady is, in fact, what the Germans call a Herostrat?
And, to close off, something I was reminded of by the hilarious Guardian title: