Don't blame me, I'm only the messenger.
Your colleague Withnail had said: "It's likely that Rudy didn't want to take any items which carried a risk of linking him to the crime scene, once the burglary had turned into a rape and murder."
So it's normal that I apply "a rigorously evidence-based, science-first approach" (your self-described method of work) to such speculation by Withnail.
Let's see, when Rudy sat down on the pink toilet seat in the other part of the house he had already likely been in the house at least for a few minutes (I mean, he would be a criminally poor criminal if he got the stomach cramps just when he was stuck on the outer wall in the view of passers by, and had to tumble into Filomena's room and go running to the bathroom on the far side of the house and sit down to intestinal bliss).
Although Charlie seems now to be painting a psychological profile of Rudy to be that of some serial killer called Ramirez, for the sake of argument here, let's just assume that he's a run of the mill human-fly burglar who initially only wanted to steal a computer or two (which the FOAKers seem to insist is part of a criminal past in Rudy).
So, there's a professional burglar who has arrived unscathed in Filomena's room, and he hasn't yet felt the need to run to the bathroom ..... what do burglars do? Why they steal things!! and since a portable computer, for as small as it may be won't fit into your Levis jeans hip pocket, any burglar worth his salt will have a bag or backpack to put his loot into, and he'll start putting things into that bag.
Or is the latest version of FOAKer speculation that he sat down and watched an Italian soap opera on TV, waiting for someone to come home in order to rape and murder them?
So, Kevin, let's get back to Withnail's theory which has troubled you: if Rudy wasn't going to take anything with him when he ran out of the cottage (thereby reducing his chances - according to Withnail - of getting associated with the crime, in spite of DNA and shoeprints which he did leave), then he would have had to unload and leave behind any burglar items which he had already tucked away.
Unless if you want to go the way of him tumbling into Filomena's room with stomach cramps which have seized him in the last three minutes while he was on the outer wall, trashing the room as he flails about orienting himself, not touching any of the burglarable material, running to the farthest away toilet, and just then an unsuspecting Meredith decides to enter the front door, not having seen the broken window from the outside nor the light in the other bathroom.