I think I agree with you that this is bogus statistics.

It sounds like the underlying claim is "there are wild zebras here and this is interesting." And the question isn't how many zebras were observed compared to the number of horses, the real question is the probability of recording a zebra when you just saw a horse with dust on it. Which yes, Fisher's exact test won't tell you.

My sense is that many researchers are confused about statistics, and so the prior for "author is confused and the statistical machinery is being misapplied" should be high.