I think ESP would tell you what the guitar is made out of, just dont mention the re-finish!
A Veneer IS a thin peice of wood, you didnt mix up your words.
My friend has an ESP like that, same colour and hardware, although i think his is the EC1000, its a carved top anyway. Very nice guitar.
Erm, yes, you wont know if ESP will give you the info unless you ask them. That seems to be your best bet. (well to me it seems like that)