My (admittedly limited) understanding of this is that the author may be correct in general he is probably wrong about the particulars. He seems to be talking about the effects of metacentric height (GM), essentially the vertical difference between Centre of Gravity (CG) and the Metacentre which is related to the interior volume of the vessel. Centre of Buoyancy (CB) will be below CG in a stable floating vessel. High values for GM generally mean stability in roll.
The author seems to imply that when a submarine is running decks-awash, the CG=CB and therefore roll stability is lost. But since the boat retains positive buoyancy, this is impossible as the interior and the unflooded surface areas of the ballast tanks remain free of water. The boat may be more sensitive to roll but sufficient reserve buoyancy and a positive GM should exist to prevent capsizing.
I recall that both Prien mentioned running decks awash in Scapa and Kretchmer used the technique in night surface attacks when conditions were favourable. It was common to flood down when loading external torpedoes into the boat as well, a difficult evolution in any sort of seaway.
Paul Schratz in
Submarine Commander mentions his captain flooding down his Fleet Boat to facilitate rescuing pilots while life-guarding but I don't recall him mentioning the prevailing sea state.
For more on ship stability and metacentric height see:
http://en.wikipedia.org/wiki/Metacentric_height
http://www.gwpda.org/naval/gmdefn.htm
http://www.navweaps.com/index_tech/tech-009.htm