Faithlilly's explanation.
The Met think it was Gerry wot dunnit. They think JT lied about her sighting. They think Gerry got her to say she saw a man carrying a child whilst at the same time as she saw Gerry talking to Jez Wilkins, a man that was dressed similar to him, reason being Gerry knew he'd been spotted by the Smiths carrying the uncovered corpse of his daughter through the streets of PdL and just prior to the alarm being raised re her disappearance and moments before he dumped the child's body in a bin, hoping it would soon be discovered and the sedatives in it blamed on an abductor. Sadly for Gerry it all went horribly wrong when the bin collectors took the body away and dumped it in landfill never to be found again. No one knows why JT would agree to take part in such an awful lie but hey ho, perhaps she had a crush on Gerry. He later dobbed her right in it by claiming he never saw her walking past, but then that had something to do with possibly being observed by someone else on a balcony. You never can be too sure who's watching and far better to dob your only alibi in it than risk being rumbled by an eagle eyed holiday maker who may or may not exist.
So anyway, in order to completely freak out JT and the McCanns, the Met invented Crecheman and intreoduced him to the nation on the Crimewatch programme. Unfortunately it didn't freak them out enough and neither has cracked so far. Never mind, the Met want us to look for Smithman (them knowing all along it's Gerry) and that's why they issued a couple of not-very-good e-fits of Gerry McCann, so the next time you see Gerry at the supermarket or at the hospital be sure to call Operation Grange and report that you have found Smithman.
It all makes perfect sense dunnit?