I'm a little befuddled by all the talk about edges, rust, beat to shit, etc. Who cares? That's like me finding a rat tail in my soup at McDonalds and someone telling me that I should have gone to a 4-star restaurant, because the soup would have been better. McDonalds should still take care of me, as a customer, for their problem (the rat tail).
Taking the OP at his word:
1) he bought them new
2) they haven't had a base grind before
3) the photo shows very thin base material
I'd have a problem with that thin of a base material also.
However, the OP will have a hard time warrantying, because he didn't handle the problem when it first arose - he didn't send photos of the thin base material to Volkl/shop right when the core shot happened, instead he got them repaired, continued to ski on them, and is now complaining once the core shot has ripped out and further damage has happened.
It does sound like Volkl responded to him, saying that the thickness of the base material looked normal, which, IMO, is a load of bull. That sort of response from Volkl is pretty rediculous, and a good reason to never buy from Volkl again.
OP, you'd be better off buying from a company that takes pride in the durability of their skis - Praxis, ON3P, PMGear and Moment. These 4 companies are well-known for having thick edges, thick base material, and using some of the hardest base material they can find. If you want another manufacturer's skis, request specs on base material thickness, style (i.e. hardness), and edge thickness. I too have been pretty displeased with the thickness of base material and edge material of the major brands, but, then again, I ski hard and don't like to baby my skis. I also go to a shop that I trust - one that prides itself in grinding as little as possible (or not at all) when tuning, specifically to increase longetivity.