Eurogamer seems to have confirmed the PS4 Slim on Gumtree was the real deal. How? By sending someone round to the buyer to look at it. They promise to have more on the updated console soon.
Here's a video of the thing booting up:
It looks like my conclusion was completely wrong, but you can't blame me for being sceptical. It'll be interesting to get a proper look and see how the new console actually compares to its older brother.