Surely the police's function is to find evidence that such a link exists, not to try and exclude one that may not exist in the first place..
Sorry, my post got garbled.
Yes, it'a two-way process, whether it concerns the dogs or not.
Eddie's alerts remain a possibility in the apartment, but then as he couldn't talk and numerous other irrelevant explanations exist, then the alerts might be more significant if all other possibilities had been methodically excluded.
The same with other indications, e.g., witnesses thinking they'd seen someone in the area; an unusual mast indicating a phone ping, or supposed discrepancies between statements.
If other witnesses are sure that x wasn't the person who others had seen, then there's a question mark. If a phone ping can be explained by a stronger signal from one mast in the capture zone when the other mast signal was weak, that's another question mark. If statements weren't verbatim (which they weren't), and bearing in mind the chaos prevalent at the time, that raises other question marks.
It's a jigsaw puzzle without the full, completed, image conveniently illustrated on the box. There are always going to be pieces that you leave to one side because you don't know where they may fit, nor whether they are part of the same puzzle or not.
Presenting leafy tree pieces as a logical place to fit in a blue sky because there's an unfilled space is a possibility if the full image is a painting by a modern artist, but that would seem less likely if the full image is a painting depicting natural scenery.