Maybe you could read that part? I re-read it and can't quite figure out what he means. I'll e-mail him if all else failes and ask him what he means.
Don't bother. I read a little more extensively - not all of it, but enough to tell that he doesn't know what he's talking about.
I had initially only read the first paragraph under "Magnetic time suspension", where he mentions magnetic refrigerators. That paragraph was OK, though irrelevant. But I doubt he really understood it either. In your refrigerator, the freon gets cycled in temperature: it cools when evaporated, thereby cooling your refrigerator inside, then gets heated when it's compressed back into a liquid, dumping the heat out the backside of your refrigerator. It's that cycling which provides cooling power. The same sort of cycling happens with a magnetic refrigerator too: the magnetic material heats up (dumping energy) when exposed to a strong magnetic field, then cools down (sucking up energy) when removed from that field (the energy required to run it comes from the fact that after the magnetic material has dumped heat in the magnetic field, it is magnetized and it takes work to move it out of the field - no violations of thermodynamics occur, just as with a freon refrigerator). In other words, simply applying a magnetic field, regardless of how big it is, can never KEEP something cold directly. You only get the cooling power by cycling something in and out of the field, which means its temperature cycles too.
In the following paragraph where he talks about an atom trap, it becomes quite clear that he's really confused. It's not the magnetic field which cools the atoms, it's the lasers. The lasers are slightly detuned from the absorption spectra of the atoms, so that the atoms don't absorb very well when sitting still. If they're moving towards one of the lasers, however, the doppler shift increases the absorption, so that the atom gets pushed back and slowed down. The laser light thus discourages the atoms from moving, hence the cooling. The purpose of the magnetic field is not to cool the atoms, but to trap them spatially by tuning the absorption frequency of atoms (the orbits of the electrons shift energy in the presence of a magnetic field). By arranging the magnets in a particular way, you create a spot of zero magnetic field in the center, and increasing field as you move away from center. So what happens is that atoms which drift away from the center are more likely to absorb light, and hence get pushed back towards the center (there's also some dependence on the polarization to ensure that it's the light pushing back towards center and not away from the center which gets absorbed, but that's not important now). In other words, magnetic fields do NOT do the cooling, they're only there to help confine the atoms so that they don't all slowly drift down to the bottom of your chamber under the force of gravity.
Later on he says, "For the purpose of this thought experiment, imagine that the chamber uses magnetic field technology where superconducting magnets can literally halt the vibrations of every atom within its chamber." But this statement is nonsense. Magnetic fields do not halt the vibration of atoms. They cannot. There's only two things they can ever do: align magnetic moments, and (if there's a gradient to the field) exert a net force on those moments. But aligning magnetic moments in a field doesn't keep them cold, they will still return to the temperature of their surrounding environment, and being aligned doesn't prevent them from moving around. And you can't just apply a large force to the body to get the atoms to stop moving either, or you'll end up with a squished body which isn't moving because it's dead. It would be like trying to refrigerate something by putting it in a trash compactor, you're not going to get the results you're looking for. And there's no possibility of doing a laser trap (ala the supercooled atoms) with a human body either, since we're opaque and absorb broad spectra, not just specific frequencies. And in any case, the body isn't really magnetic (it's very weakly diamagnetic), which means that magnetic fields hardly do anything noticeable to your body. That's why you can sit comfortably in an MRI machine, but if anything magnetic gets brough near it serious problems occur.
In short: magnets can't do what he seems to think they can do, and they can't freeze a body from the inside out. If you want to cryogenically suspend someone, you've got to do it the hard way, from the outside in. The closest thing to freezing from the inside would be a cryogenic enema.