I got an unusual GTX 560 Ti

[Panormitis]

I ended up with a fake card a couple weeks ago too. My "GTX460" was basically a GT430 with 256MB of memory. I got my money back though.

Fortunately you got your money back. Was it from ebay or aliexpress?

If you remove the HSF, what does the core say?

Take the cooler off and take a pic of what it says on the GPU. Its very rare to happen but not uncommon for a graphics card to have a vBIOS thats not fully functional but the only cases like that I've heard / seen are ES samples. As this card is supposed to be OEM, who knows, maybe its just got a ES vBIOS on it. Its a long shot though, I think you have more than likely been duped.

If I remove the heatsink I'll probably have to remove the old thermal paste and apply new one, right? I don't have thermal paste right now to try this, but I'll get some in the next days and I'll attempt this. I'm curious to see what GPU chip is underneath.
I'm planning to buy some Arctic Cooling MX-4, is it good enough for this, any suggestions?