He admitted being there when she died. Not much else is needed.
The absence of evidence proves Rudi didn't break into the cottage but the absence of evidence doesn't prove that Amanda wasn't part of the murder. This is the hypocrisy of both sides.
No, it's more complicated than that.
In the abstract, absence of evidence is not evidence of absence, but that formulation is not an absolute, it's dependent on how hard you looked. Making a determined effort to eliminate possibilities and accumulate data does amount to evidence of absence. In other words evidence of absence (looking for it hard and competently and not finding it) reduces the probability that evidence actually exists, but never becomes an absolute either, as you can't look everywhere and there may be factors beyond current understanding. For example the probability that bigfoot exists is so extraordinarily low (in part) because there's never been any remains of one found, and the human race has found copious evidence of beings that died out 65 million years ago, (dinosaurs) not to mention all the rare and difficult to find species that we have.
That lack of evidence where it should exist, and we have every reason to think we could and should find it (and people have certainly been looking!) does amount to evidence of absence. However it is still theoretically possible that they do exist, or existed, it's just highly unlikely that a being that seems to have been sighted so many times has never actually been found physically, thus obviously must reside where humans would find solid evidence and not just 'sightings' or 'tracks' that could very well be something else, and almost certainly are.
However, contrast that with the possibility that there is other intelligent life in the entire universe, however don't misunderstand and think I mean that any have actually been here. I'm talking about the entirety of the universe and the possibility that somewhere in those more than 100 billion stars (or so as a ballpark guesstimate--they vary of course) per more than a hundred billion galaxies there is another form of intelligent life. That probability is higher because we know (almost) nothing about much of the universe, we cannot and have not been able to look very hard. Allow me to again note that doesn't mean I think any have actually been here, we do know enough to realize that space is so goddamn big and the inability to travel those distances or even communicate over them means there could easily be trillions of lifeforms out there and none of them able to contact any others any more than an ant in Antarctica could ever get to the north pole.
The fact that the murder room was gone over twice and absolutely nothing found of Amanda but so many trace elements of Rudy strongly suggests they looked very hard where evidence of murder might be found, down to the picogram, and could find nothing whatsoever of who they claimed was a key contributor. That's extremely suggestive that Amanda was not involved in the (physical act) murder at all. However it is quite possible, perhaps even likely, that were the entire room gone over and every last picogram amplified and analyzed they might well find Amanda's DNA in Meredith's room, it just wouldn't mean anything because she lived there and DNA not related to the murder may well be found in such trace elements. Where evidence of murder was likely to be found, they found nothing, Raffaele's anomalous Y-haplotype on the bra clasp no more meaningful than the other three men's despite it's (technically) more robust nature due to the circumstances in which it was found and the context of the 'investigation' at that point, but also especially because that's all that was found. The idea that Raffaele and Amanda were in that room is akin to the idea that bigfoot exists.
Regarding the burglary, many indications suggest that Rudy breaking in is the most probable explanation, that his DNA wasn't found (at and nearby the window)is not surprising being as they didn't look down to the picogram there, and didn't appear too interested in looking going by the time it took them to analyze some of the results.