As far as I can tell, no argument is made in the paper that human cryopreservation causes information-theoretic death, and neither of these repair options are discussed at all.
Cryonauts probably have enough information to reconstruct them to the point where childhood memories can be recovered. I don't think claiming otherwise would be a sensible critique. IMO, sceptics are better off sticking to looking at the costs.
Luke Parrish points me to what is clearly by far the most serious critique of cryonics ever written: a 57-page treatment by Evelina Martinenaite and Juliette Tavenier, presented as a 3rd semester project at Roskilde University in Denmark supervised by Ole Andersen.
Full paper