Regarding inherited fertility in animals
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.