Some mules (a very few - something like 60 in the past 500 years) are actually fertile. Does that change your mind about whether or not horses and donkeys are distinct species?

The reality is that there is no good definition of species, and cannot be. Yours is a common one, but has a lot of problems - declaring wolves and pomeranians the same species is a tough bridge to cross for most people: you've made the definition so broad it means little. Biology is messy and in the real world there are no clear-cut, convenient dividing lines.

Another problem with that definition is that there is no transitivity in real biology. Animal A and Animal B may be able to produce fertile offspring. Animal B and Animal C may be able to produce fertile offspring. But Animal A and Animal D [a sibling of Animal C, thanks KMag for that point!] may not be able to.

Of course, we also would find it strange to declare that two humans incapable of producing fertile (or any) offspring different species.

You may want to introduce a fourth individual in your example, so it's not limited to species (mostly amphibians and fish) that are able to morph sex or hermaphroditic species (some molluscs, snails, etc.). Otherwise, the example is trivially true for all mammalian species that I'm aware of; for humans, if Arthur and Betty can easily breed fertile offspring, and Betty and Clive can easily breed fertile offspring... then Arthur and Clive are going to have a very low breeding success rate without technological assistance.