Wouldn't Stoat have been in jail and unable to get to Goren's desk?
Depends on how long the rat had been there. Stoat could have left it in the desk earlier, before he was arrested.
If it had been there any length of time, everyone would've known it was there from the smell alone. It also didn't show any signs of decay. Clearly it had to have been placed there recently.
The rat could have been fake.