It struck me as interesting because there's been a 'Forbidden Planet and TOS - same continuity!' thread on the TOS forum every few years foras long as I can remember (previous incarnations featured more ENT-bashing and less discussion of Marliyn Monroe, so this is an improvement).
This is the first I've read about someone speculating that FP was a prequel to TOS (although I'm new here so you can take that into account). Nevertheless, although I agree with Christopher that FP is it's own animal, I think that TOS Purist's "thought experiment" is just that - a fun "what-if" moment in that he's not downright exclaiming that it is in fact a TOS prequel, just what people think of the idea.
So, in the spirit of fun, I also think it would have made a good TOS prequel, with the following caveats:
1. You'd have to eliminate ENTERPRISE from the equation (which many people don't seem to have a problem doing

), and
2. You'd have to either ignore FP's opening history of manned spaceflight, or ignore TOS's history of manned spaceflight it establishes later in the series. And TNG's. And DS9's. And VOYAGER's.
Anyway, all the hallmarks of early TOS are there. A united planetary organization; similar tech, weapons, uniforms, sets; and of course the triad of the commander, first officer and doctor. Heck, it even takes place in the same century. Not to mention that it's a damn fine movie.