Given the amount of work, time and materials involved alone in restoring the tape deck, compared to the cost of buying one off eBay (for under $50), I'd say if it was real, they must be expecting ad-revenue from YouTube to fund their effort because it looks to be a crazy use of time and energy. I know some people have a passion and hobby for doing this type of work even if it is not economically feasible and they will end up losing more money than they get, in exchange for the pleasure and self-satisfaction of pulling off the restoration. Nevertheless, it just looks too good to be true. If this was real, I would be very impressed. I haven't watched the "busted" video yet, I'll have to see what clues they used to back their claims but I wouldn't be surprised that these types of "fakes" videos exist. Call them "Faketertainment".
[ADDED:]
One more thought... one good argument for thinking it is a fake is the amount of work invested in this device before any basic electronics troubleshooting (unless it was not included in the video). Imagine you find a piece of old junk covered in mud and rust on the side of a river/lake and decide you want to restore it. Why was it junked? Does a perfectly good set get dumped on the side of the river? Perhaps there are issues with it? Before you invest all that time and energy, would you not do some basic electronic investigation into the worthiness of the device? I mean obviously you have to clean off the mud and dry it... I get it. But before you start dismantling the tape deck mechanisms and polishing them all, wouldn't you want to just power up the board and see if it shows signs of life?