I think that is very likely Mike.
The cover up started from a very early stage, involving the timing of the two shots, where the police were prepared to accept that the second shot occurred as a result of recoil. It was an explanation that was introduced, in my opinion, to cover for Sheila being shot for the second time, after the police surgeon confirmed Sheila to be dead, and his reference to there only being one wound on her throat at that stage (8:44am)...
I believe that the police know that Sheila shot and killed the others, and that they also know that Jeremy did not shoot dead his sister in the bedroom and stage manage her body on the floor to make it look like she had taken her own life. The police know that this is not true, because they originally found Sheila's body downstairs in the kitchen, and later it ended upstairs in the bedroom on the bed, and the police moved it onto the bedroom floor, themselves...