Hmmm, I keep coming back to this auction-I'm intrigued.
Re the earlier points about headstock/ binding/ checking; I have a '56 X500, like this, but sunburst, so I can compare them - the headstock lacquer on mine is breaking up just like this example, so that seems authentic, but the body finish on mine is also quite checked, as you'd expect, and the binding is quite yellow, as you'd expect for 55 year old nitro lacquer. I just can't see how this example can have snow-white binding and a relatively white top, unless it is a refinish or possibly has been stored in the dark. 55 year old nitro lacquer is light brown!!! The other odd-looking thing is the switch tip, which is also quite light-coloured, whereas the original switch tip on my '56 is mud-coloured. Could be a replacement, of course.
It is a great-looking guitar, though, and ( assuming it's really a laminated top, not carved ) might still fetch reasonable money, even if it is a refinished example. Personally I think refinished guitars can be excellent value player's instruments, if priced as such. We'll see!