I have just googled the true story that this was based on. It didn't exactly happen this way.

Dr. Howard Kelley was a struggling medical student selling magazines door to door. He reached a small town and was very hungry and asked for a glass of water from a house of a poor family. He was given a glass of milk instead.

Later on while he became a high ranking doctor at John Hopkins Hospital a sick old lady was admitted from that small town and he found out it was the same lady who gave him a glass of milk. This was an era prior to social security and welfare and surely the poor lady's family will be in for a lifelong financial debt. And that's how he wrote in the bill the phrase "paid with a glass of milk many years ago".