If an animal is fertile does it follow that both its parents of the same species (not necessarily the same species of the offspring)? Was it Mayer who said a fertile male and fertile female of two different species, if they 'reproduce' and the offspring survives it won't be fertile. Reproductive isolation I think this is called. So if an animal is fertile then both its parents should be of the same species, right?
No it isn't necessary that the parents should be of the same species. Mules (male donkey X female horse) have been found to be fertile (reference). The wikipedia page on hybrids lists many inter-species hybrids that are fertile including Beefalo (Domestic male cattle X american bison). There are also many canine hybrids which are fertile. Wholphins have been found to be fertile.
A wholphin or wolphin is an extremely rare hybrid born from a mating of a female bottlenose dolphin (Tursiops truncatus) with a male false killer whale (Pseudorca crassidens).
So in short, for a hybrid offspring to be fertile, it doesn't necessarily need to be of the same species.