"Salt", in Roman times, was what was called the brains within the human head, or perhaps was what they believed filled the human head. The Latin expression was thus a proverb of sorts--meaning that, in everything, we should use at least a grain of intelligence or understanding. It was, then, a recall to common sense--a reminder of prudence and reflection before action.
To take 'it' with a grain of salt now means 'to accept a thing less than fully.' The Oxford English Dictionary dates this usage back to 1647. The terms are not dissimilar -- both essentially mean to regard certain things with some understanding and common sense.