Oh interesting. I had no idea

Theoretically that wouldn't be a killer issue, since fertile mules are extremely rare, so you could refine the definition to say "is very very likely to produce fertile offspring" (while horses and donkeys breeding is not).

The bigger problem are things that have massive morphological differences but can still successfully interbreed, such as dogs, coyotes and wolves. They produce fertile hybrids and there is good evidence that this occasionally happens in the wild, but nevertheless it is rare and they have clear, stable morphological distinctions, even in areas where they overlap.

Even worse, that definition is entirely useless for paleontology, as it is impossible to know if two individuals species could even interbreed, nevermind knowing if their offspring would be fertile. Even modern genetic evidence (which is extremely rare for fossils anyway) is very open to interpretation on the matter of potential interbreeding ("Neanderthal" genes in modern humans could more or less as easily be common genes older than both H. Sapiens and Neanderthals - we have far too little evidence to be sure, and no chance of genetic material from an older ancestor).

If neanderthal or denisovan genes were ancestral, you would be able to find them broadly in African genomes and some of them wouldn't carry adaptations to environments not found in Africa. Instead they reinforce (and inform) our understanding of early human populations out of Africa.