The police, of course, were sure of nothing - that's why they had to build a circumstantial case!
They were "sure" a green ski mask was a black balaclava. They were "sure" a knife used for opening boxes had "disappeared" until it was pointed out to them that they had photos of it ... so they must have it.
By August 14th they had reports of jackets - a shiny green bomber jacket with orange lining, a "fishing style jacket" with matching trousers and a dark coloured jacket, maybe green, could have been a Parka "but I only say that because of the length."
The day wasn't "cooler, wet and dreich" - it was a day of changeable weather, warm and sunny in the early evening with a couple of sudden downpours - I was sitting outside on the deck reading a book after dinner when, all of a sudden, it started to rain. No miracles required, just typical Scottish weather.
Speculation about when he "might have got the jacket" is just that - speculation, with no evidence to support it. Of those who "remembered" Luke in a Parka, how many had not seen the media coverage of him in a Parka? The influence of such high profile coverage, for such a prolonged time, on recall cannot be ignored.
If the police "knew it had disappeared," why did it take them 9 months to start looking for it? They'd already raided Luke's house twice by then and had a liaison officer in place for six weeks over July and August. What took them so long?
F & W's sighting wasn't clear at all (see above) - that is the only reference, in the early statements from both of them, to a Parka - and all it says is, "it could have been."
I didn't introduce MK into the equation - he introduced himself, telling a friend he'd been spoken to by the police because he was "running on the Newbattle Road that night," when he hadn't spoken to the police at all. (This was before anyone had even heard of SF). However, his ownership of a Parka prior to the murder isn't in question so, yes, if it "could have been" a Parka that F & W saw and MK was on the Newbattle Road that evening, it equally "could have been" MK that they saw. Hardly solid evidence of anything and that's my point. None of the "evidence" in this case stands up to even the slightest scrutiny.
Could have been MK, could have been Luke, the girl "could have been Jodi", could have been 5 o'clock or 5.30 or 4.50, could have been 4.39 - 4.54 or an hour later, could have taken this route or that route back from the supermarket, could have been a blue hoodie with lighter blue bootcut jeans, could have left at 6 o'clock or 5.40 to go to Costco ... proven beyond a reasonable doubt? Nowhere near it.