I think I have the answer to whether and how drinking seawater can cause madness. Funnily enough, a similar question was already answered in The Straight Dope - "What would happen if I drank seawater?"; I managed to put in the wrong search words or something when I tried to find it.
That madness ensues is only implied though, in a quote from Bill Bryson which effectively says that the severe dehydration causes your brain cells (among other things) to break down.
Which leads me to think that the saying really ought to go "drinking seawater makes you really really sick and maybe die".