What does the phrase mean- to take something with a “grain of salt” ?

To be skeptical about a statement made, to take it with a grain of salt.

Here’s OED.

with a grain of salt [= mod.L. cum grano salis]: (to accept a statement) with a certain amount of reserve. Also in similar phrases, now esp. with a pinch of salt.

1647 TRAPP Comm. Rev. vi. 11 This is to be taken with a grain of salt. (That’s the earliest instance given in the OED).

Sounds to me like the recommendation of a mediaeval apothecary........

Is there any indication of a connection between taking (eating) something with a very small amount of salt and being sceptical?  I can’t see how the effect of salt on food is remotely similar, metaphorically, to the effect of scepticism on an opinion.

Just updated the Big List entry yesterday:

http://www.wordorigins.org/index.php/site/comments/with_a_grain_of_salt/

Needs another (slight) edit: Cn. Pompeius stands for Gnaeus Pompeius, not Cneius Pompeius.  ("C." and “Cn.” for Gaius and Gnaeus were survivals from a time before the letters C and G were differentiated in Latin orthography.)