Re: But if it's been obtained illegally, it may not in fact be evidence
Aren't you conflating two separate, if related issues there? It is of course vitally important to establish the accuracy of evidence, but there seems no especial reason why legally gathered must always be truthful and reliable, and illegally gathered evidence automatically unreliable or misleading.
I'm quite sure that a depressing number of trials end up with the wrong verdict even if every scrap of evidence has been gathered in strict obedience to the rules. It may be that prosecutions who break the rules of gathering evidence are also more liable to fabricate evidence, but association isn't causation.