I'm inclined to believe that (most) people see what they're told/led to believe they'll see. i.e. JB painted a very clear picture of Sheila and her mental instability, which included a previous suicide attempt which has never been verified, so obviously, when police went in and saw her with a gun draped across her, their first thought would have been suicide. It would have taken a very brave person to stand out against the general consensus and claim it was something other.
He called her a nutter, do lally, looney, is having treatment, should be locked up, didn't like him, knew how to use all the weapons at WHF, he didn't like her.
That was after he told them about Nevill's call.
Then he asked Bews & Miller to go inside!