The 'coincidence theory' of Jeremy being the killer and telling Julie the same false information that the police told AE. Has no plausible basis in reality. It only works in the fictional game of "lets make things fit" by blaming Jeremy for Julies lies.
The bit about Sheila and June being found dead on the bed with a bible between them was going the rounds that first morning at Bourtree Cottage, Goldhanger and did not emanate exclusively from Julie.