Well it could except they are arguing that the police had been in conversation with Sheila but the reference is to Jeremy and no one said they were talking to him through a loud hailer. The conversation with Jeremy, took place just before they challenged the house.
Not having watched the video,I'd have thought that police would first have handed the loudhailer to Jeremy for him to speak to his sister,as happens when there's a siege situation. That would have clinched the whole case.
The thing that makes me believe that Sheila was alive,are the notes she wrote about " police being there ",which was a pre-emptive move on her part.