It may be that they don't actually interpret evidence at all!
I have explained these erroneous conclusions in the past as being down to the 'affirming the consequent' fallacy:
If P then Q;However, there's another version of this (the proper name of which I can't remember off the top of my head):
Q therefore P. (which is invalid reasoning).
If, and only if, P then Q;I wonder just how many people are making the second mistake?
Q therefore P. (which is valid reasoning).
I often find that when someone has come to a conclusion on an issue (the psychic was genuine, etc.) and you offer alternative possible explanations, they tend to dismiss anything else that is offered up. It's a fallacy of exclusion as they, either deliberately or unwittingly, exclude anything that destroys the 'if and only if' premise of their argument.
That's another possibility anyway.