from what i understand that ordinance is only application if they are washing it on public property. his own driveway is private property and whether or not it's in "public view" doesn't change it to be anything other than private property.
the guy handling it did very well asking for the ticket right then and not pursuing any sort of argument, fighting it in court is the best course of action.
as for the whole license plate thing, as long as the car isn't being operated on a public motorway (which it isn't in the video) then a ticket can't be issued.