So a mentor of mine was telling me a story about how in the Roman Empire, if a Roman citizen were traveling down the road within the bounds of the Empire and passed by a non-Roman citizen, that the non-Roman was obligated to put down whatever it was that they were doing and carry or help transport the cargo of the Roman citizen for one mile if they were called to do so. Is there any truth to this story?
I suspect you or your mentor has made things a little unclear in the retelling. The practice referred to is basically pressing someone into service. In the Greek texts it utilises a word derived from Persian royal-messengers. Messengers, naturally, with the right to requisition fresh mounts. EA Judge in Horsley, New Documents Illustrating Early Christianity vol 1, 36-45 discusses an edict for this practise in Pisidia. Josephus talks about the forced requisition of animals by the army in Antiquities 13.52, so it certainly existed as a practice. Whether it had the force of law was another question. Most instances appear to be related to military forces, not to Roman citizens versus non-citizens. The context of its usage in the Biblical literature has to do with Roman occupying forces and (the sense that) Judea was an occupied territory. The restriction of one mile appears to come from Matthew 5:41, but apart from that reference I am not sure that there is any evidence to suggest that that was the limitation, and even that biblical reference does not state that the limit was one mile (very unlikely).