Wrong. In the absence of evidence, rationality dictates that you say "There is no evidence to suggest the truth of X, and I cannot, with any amount of certainty say, that X does not exist."
I think your statement is a bit broad. If X implies the existence (or likely existence) of something else, then the absence of that "something else" is evidence of the absence of X.
For example, if you find no mouse droppings or chewed food packages in your house, then this is evidence that you have no mice. If you don't see divine miracles occasionally, then this is evidence that you do not have a miracle-wielding God.
Also, the absence of evidence can imply absence of
knowledge, which means that there's no valid basis to suggest the truth of X in the first place. The classic example of this is
Russell's Teapot: there may be no evidence for me to explicitly disprove the existence of a small teapot between the Earth and Mars, but there is also no evidence to let you conclude that there's a teapot there in the first place.
IOW, when we're evaluating a claim,
sometimes absence of evidence is not evidence of absence, but sometimes it is. And absence of evidence is
always evidence that you just pulled the claim out of your butt.
Edit: actually, now that I think about it, your original statement is entirely inaccurate. In a statistical sense, when you look at all the attempts for evidence together, every sample that contains no evidence of X is evidence against X
with a very specific degree of certainty. That degree of certainty won't ever get to 100% until you've exhaustively looked everywhere, but even after one observation, it's greater than zero.
Well, that puts a hitch in Native American spirituality, since their "Great Spirit" is a pantheistic deity. A sentience that infuses everything in existence. I think that's as valid as any other definition of "god" and more plausible than most.
Which is not to say I share that belief, but I relate to it much more easily than I can relate to the idea of some bearded humanoid floating around in space and smiting stuff he doesn't like.
Whether it's more or less plausible than other religious models isn't really the issue; it's a question of the validity of terminology.
As an analogy, take the claim "my house is filled with poison gas". By itself, I'd say it's very implausible; it's much more plausible to say that it's probably filled with air. However, this doesn't mean that it's valid to call air "poision gas" to shoehorn the more likely situation into the original claim.
But re-thinking my original statement, maybe it would be fairer to say that how a person relates to the universe affects whether it's reasonable to call it "god" or not. I suppose that if a person actually worships the universe as a god, that's one thing, but if we're talking about "god" as a label for the universe that someone has simply feeled like anthropomorphizing a bit by endowing it with perceived thoughts and feelings, then I don't think it's valid to call the universe "god" in that case.