This is speculation but I wonder whether the thing you've heard about rams and salt relates to urinary calculi.
The bit that is not speculation is that if male lambs are eating a lot of concentrate they can get urinary calculi, which block the urinary tract and are very painful. To avoid these, there should always be plentiful water, and the feed should be specifically suitable for tups, not a ewe feed.
Views differ as to whether it is useful to put out salt for tups being fed hard; some think the salt encourages the tups to drink more, which helps to avoid the calculi, and I'm wondering whether some think that the salt itself can contribute to the formation of calculi. Or maybe some of the feed licks, as opposed to salt or straight mineral licks, can be bad for males, if they don't have the formulation which reduces the incidence of calculi.
Either way, if the tups aren't being fed hard and are getting a suitable feed or no supplementary feed, and have symptoms which suggest a lack of some minerals, then I personally would be giving them minerals in one form or another. I am also of the schools of thought that a) all sheep need fresh water always available and b) Himalayan rock salt is magical and should be available to all livestock at all times.