It's not really a cover up though, as long as everyone at 34 Fairview agrees John didn't come in the house and Karen hit him. All Higgins would need to do is to tell Proctor they know Karen hit him with her car but there's not enough evidence to prove it and he agrees to manipulate evidence. Hell, maybe they didn't even ask Proctor to do anything and he decided he needed more evidence to make a conviction against Karen stick.That still involves everyone lying, and somehow managing to firstly, concoct a plan of cover up in that short space of time, including outsiders to help with planting pieces of taillight etc.
I don't have an explanation for the glass in John's face though, am I right in thinking a cocktail glass was found but it didn't come from any of the bars they had been to? Was the glass smashed?