Etymology of "metes"

Can anyone tell me if the etymology of "metes," that I read or heard some years ago has any basis in fact. The word mete means not only to measure, as in the phrase "metes and bounds" used in property descriptions, but also to allot, or dole out, as in the phrase to mete out punishment. The supposed connection between the two meanings derives from a reputed practice where literacy was rare (and mapmaking inaccurate) of taking the youngest child of a village to the points that mark the outline of a piece of property and beating him soundly at each one.

That is, at each marker a tree, a large boulder, etc. punishment would be meted out to the child. Consequently, he would keep a vivid recollection of the places of pain and punishment throughout his life and, so the theory went be a reliable witness to the location of the boundaries of property in the village. Being the youngest, he would be able to testify to the location of the markers for a longer period of time than the older villagers who would probably have died before him.
One example may lend some credence to this theory: Almost everyone remembers where they were, and what they were doing when JFK was assassinated, or when the Twin Towers were attacked: terrible events that remain in one's memory for years. (I must add that my memory of this etymology antedates Kennedy's assassination, so it's not a case of post hoc, ergo propter hoc.)