I'd even quite happily leave it at "Absence of evidence isn't the evidence of absesence," but with the caveat that absence of evidence is also no reason to assume that something exists. Yes, there is always some tiny chance that we just didn't look in the one hidden cave where the world's only yeti lives, or we didn't stumble upon the exact spot where the dimensional portal to Santa's workshop is, but in the meantime there is also no rational reason to believe in them without any evidence that requires a yet or Santa to explain.
Really, it's just Occam's Razor, and I think most people find it quite natural to apply it to anything except their pet woowoo.
E.g., if I told someone that mom is Wonder Woman and has an invisible airplane, they would want some evidence before they believe either. "You can't disprove that she has an invisible plane" may be technically correct, but it also doesn't mean any rational person should believe it just because lack of evidence for such an invisible plane isn't evidence of absence of said plane.
E.g., to take a sadly more real example, it was (and still is) impossible to prove that people don't fly on a broomstick to the witches' sabbath. You'd think that at least something like her husband testifying that she was at home in bed at the supposed night would be evidence that she didn't go anywhere, or that it was outside a major market and nobody there saw anyone flying or any window or door opening on that house, but they covered that aspect too: see, witches make themselves invisible, and leave a demonic double behind in bed. So really, the best you could have was a complete absence of evidence that such a sabbath exist or anyone goes there. But conversely, I think we can agree, that then there is no reason to assume that one does exist.