It wasn't clear as to where George had died and officials were concerned as giving a false address on death certificate is illegal. The original address given was a fictitious LA property, probably to deter loads and loads people from turning up there to pay respects (or a few trying and get something out of it).
It turned out he had passed away in a rented house in Beverly Hills. Now this was owned by Courtney Love but had been leased by Paul. When the controversy started Paul's people denied that George had died in one of Paul's homes as he didn't OWN any in Bev Hills. It was not entirely clear whether he was still leasing at the time of George's death or not (although I seem to remember it was heavily hinted that he was and he'd lent it to George so he could die in peace and with dignity away from the eyes of the world). Even if he wasn't renting it at the time it seems too much of a coincidence that Paul wouldn't have even been the one to tell George and family about the place.
What Heather's role in this was I'm not sure. By then they were engaged though so she at least would have known. Does this mean she should be in the George film? In my opinion that all depends on how well she knew George, which I doubt was very well so no.
Oh and the authorities didn't take the matter any further.