Thinking that absence of evidence is no data is fallacious. Atrociously so. Absence of evidence is NOT absence of data. Now, the strength of evidence provided by absence varies, and absence of evidence doesn't imply evidence of everything, obviously. Would you seriously argue that if I gave medicine to a thousand people, and failed to find evidence that any of them got better, that this wasn't, in fact, evidence to the contrary?
If you were born in a windowless room, the absence of evidence of the truth outside IS effective evidence against any particular otherwise unjustified hypothetical. It's not full-proof evidence - you could be wrong. But the fact that there is no evidence to make one supposition stronger than another mutually contradictory supposition is, in fact, evidence against both of them. However, suppose one of those makes a prediction that it will - especially if one of those suppositions implies evidence supporting it should exist. Perhaps that the outside is full of bullets, and there is a good chance one should hit and enter your room several times in your lifetime. The alternative is that there are no bullets flying around outside threatening to enter your room. The fact that there is no evidence of the first case does not mean it's impossible, but it makes it less likely - it is evidence against it.
And you know what... I honestly don't even think you believe what you're claiming here. Let's test it, shall we? I make the claim that you are currently being poked in the back of the head by a burly Nordic man. Can you, without relying on absence of evidence, provide proof (of any strength) that this is not the case?
The fact is, most religions DO make ACTUAL predictions and expect ACTUAL results in the world as a whole - and for those religions, absence of any evidence of those results IS, in fact, evidence against them.
Let me offer a simple hypothetical:
You and a friend are in a room with a hundred near identical boxes. You know there is at most one red ball in one of the boxes, and have no additional information... except that your friend has no more information than you do.
Your friend points to one of the boxes and says "I believe the ball is in that box."
The lack of any evidence for this claim, combined with the number of possibilities where this is NOT true (potentially infinite, since there is no guarantee of a red ball, but at least 99) versus the number of possibilities that he is correct (1) means that said belief is, quite simply, wrong.
Note that this does not mean there is not, in fact, a red ball in the box. Under ideal circumstances, there is a 1% chance of this being the case. But the belief is still wrong, because there is no rational reason to belief that 1/100 chance over any of the others.