The reference may possibly be a martial reference. My son the classicist reports to me:
“Aristotle says that only men who have eaten salt together can truly be friends. After marching to the field of battle in full armor, the Greeks would eat salt before engaging in order to replace what they lost in sweat (since otherwise one faces debilitating cramps).”
Thus, there is something about “eating salt together” that makes men “comrades-in-arms,” that is about being in battle together, or striving together.
But that doesn’t necessarily mean that it carries the same connotation among the Greek speakers of the New Testament community.
I thought of this theory this morning. With Jesus and the apostles walking a lot in the desert, hot and sweaty, eating salt might be the best thing for them.
I nearly had a case of heat stroke because I didn’t have enough salt in my body. It’s scary.