You're basically right with respect to Turing machines, but register machines are similarly flexible, and it's certainly possible to build an actual, physical register machine. I would argue that that's insufficient to permit algorithm patents on its own, though, because the process of transforming an algorithm into a register machine can actually be mostly automated. If you come up with a clever way to do it that's better than any automated approach, sure, that's probably patentable and arguably should be. But the mere fact that such a transformation is possible shouldn't extend patent protection to the algorithm side of it.
Originally Posted by yotambien