You mean that Mugford said he faked it?
Jeremy had no reason at all to tell Julie he puked unless he did it in the context she said of saying he was a good actor liek her and had forced himself to puke so police would believe he wa supset.
Police had no reaosn to tell Julie tha the puked unless they told her to lie and say he told her that he faked it.
There would be no way for Julie to find out he puked and make it up on her own.
The notion police make the lie up for her is reidiclous the only credible account is that Jeremy told her he was acting.