I googled “virgin leather” and this thread was the first hit. Then there is a company called Virgin Leather, which is just the name of the company, not the name of the leather. Then there is a Yahoo question, which just links back to this thread. Then there are 32M hits of junk. My conclusion is that there is no such thing.
It’s not a very helpful statement.
What if he added the word “woosh”? 
I’m beginning to get the impression that the term “virgin leather” is a sales or marketing term and has nothing to do with animal hides or hide processing.
Billy - What are we talking about?
Bobby - Cow hide.
Billy - What?
Bobby - Hide. Hide. The cows outside.
Billy - Why? I’m not afraid of a cow.
So, the nauga wasn’t killed for it’s hide?
have you tried the meat? BLEAH!
I didn’t see the quote first and thought this referred to virgin meat.
The word for leather from an animal that wasn’t killed for its hide is “leather”
I know of no operation that kills any of the usual animals (cow, sheep, pig, etc) just for their hides. IME, skins are almost always a by-product of the meat industry. Sure, some exotics are killed just for their hides, I’m sure. But we aren’t really discussing kangaroos, lizards and snakes, here.
I wonder if the term is an attempt to differentiate the leather from bonded leather. Given bonded leather is made in much the same was as particle-board, made from shredded leather held together with a polymer, the distinction and use of the word “virgin” to differentiate ordinary leather is not too far removed from the use with respect to virgin wool.
Given the rise of the use of bonded leather in furniture I can imagine that some vendors might like to create a term to differentiate their product.
None e’er touched me there, said she
Not hide nor hair nor feather
And when I die a virgin I’ll be
for it has turned to leather.