This is a congenetal defect. What does congenetal defect mean? Means they were born with it. Thats ALL it means. It may or may not be genetic. You can be born/hatch with a defect and have it not be genetic at all. You can havea genetic defect and not have it show up until you're 50.
So how can you be born with something and not have it be genetic? Easy. Mistakes happen, A LOT. Think of Spina Bifida in humans. That's not genetic, but you're born with it. How does that happen? Not enough folic acid, drug use by parent, and sometimes it just happens because the baby just plain failed to grow correctly. Same with congenetal heart defects. Most congenetal defects aren't genetic at all.
Actually most genetic defects are subtle and do not result in deformities of this magnitude. IF a genetic defect did occur that WOULD result in something this drastic, the offspring would not have survived full term until hatching.
So how do you tell if a defect IS genetic or not? Statistics.
How many deformed offspring HAVE the parents produced?
The fact that they have produced ~70 offspring and had this happen ONCE would actually mean it is not genetic. If it were a genetic defect it would have been seen in higher frequency (~ 25% actually). 1/70 tells me not genetic.
The parents are distantly related and are not siblings.
So how come imbreeding is associated with birth defects? Well members of the same family line are MORE likely to have the same genes. But only MORE likely. For the most part siblings on average only have 25% of their genetic makeup in common. They can have as little as 0% and as much as 100% (as in twinning). Most though fall around 25%. Now, in the case of normal parents producing a deformed offspring, in order for it to be genetic it would HAVE to be a recessive trait. Now lets say the parents are full sibs, they have about a 25% chance of EACH animal carrying the defective gene. That means for BOTH to have it, that's 12.5% change. Not lets say that we win the lottery and both DO have this gene. Like any recessive trait, 25% of the offspring SHOULD show the trait then.
Now of course this requires that there actually BE a defective gene in this family. Most families don't have big scary defective genes that result in a deformity as drastic as this.
So if you get what I am getting at, chances are VERY slim that FULL SIBLINGS can cause a genetic defect if they breed.
So how about completely unrelated parents? Since we don't know how much their genetic makeup is the same, we can't predict the chance of a genetic defect. But since they're not related the chances of them HAVING the exact same genes are pretty slim. Thus statistically LESS likely to produce genetically defective offspring. Then again this depends a lot on the genetic diversity of the population and you get into population genetics.
Anyway, to avoid further boredom I'll summarize this. Not all defects are genetic. Imbreeding does NOT guarantee genetic defects, only slightly increases the likelihood.
Sorry, I can't help it but in undergrad my VERY favorite subjects were Genetics, Embryology and Principles of Animal Breeding. Truely fascinating things.