Don't use mythbusters as a refference, particularily when they detemine something "couldn't happen". All too often they equate their own incapability in repeating something as proof it can't be done. Sometimes they're right (especially when they take something which is proven to be impossible beforehand), but much of the time it's just juvenile bravado.

I think, though, that most of inventions of Archimedes weren't all that great. If they were, it is very likely that at least some of the better ones would find their ways into the Roman arsenal - this was, after all, how they got nearly all of their military technology.
But do we see a noticable change in Roman siege or missile technology after the fall of Syracuse? Not really. Though Archimedes was killed in the sacking of the city, much of his devices would have remained, as would people who have seen and operated them survive - at least some of them. If there was indeed as much value as believed to recover, it would be unfantomable for the Romans not to copy it.

My guess is that Archimedes and his siege engines weren't nearly as advanced as we would believe. It was probably, in 99% of the cases, just regular contemporary altillery, just more numerus and better utilised, better deployed, better led and used to a greater effect than contemporary altillery. A few extraordinary engines of limited use - like the Claw - probably cemented the myth.
Not an insignificant feat, but not nearly as special as believed.

McHrozni