So... are you saying that evidence is only evidence if you trust the source?
I don't want to talk on Persephone's behalf, but my own problem with the claim that supposed eyewitness testimony is evidence for God is that the eyewitnesses, even if their accounts are true, have no apparent tangible way of knowing that God caused what they saw. For example, the apostles talk about Jesus' walking on water. That's evidence (though by no means very strong or compelling evidence, rather like you might not be particularly convinced by me telling you that in the UK the sky looks green) that they saw someone walk on water. As to the cause, they could only possibly offer speculation or opinion.
If you allow the supernatural as a possibility, there are a myriad of myriad different potential explanations for a guy walking on water. The Judeo-Christian God as described in the Bible being the father of the man in question is only one among an unlimited number of other possible scenarios, that all seem equally likely to the one I've just mentioned. Another person's opinion isn't really evidence in the way that a factual or supposedly factual account is.
Sorry for cutting across the debate, just offering my ha'pen'orth.