There was another mary Hamilton.
This from another thread.

The Four Mary's - who were they really?
From: Keith A of Hertford - PM
Date: 18 Jul 01 - 12:33 PM

As mentioned above, the famous 4 Marys at Mary Stuart's court did not include a Mary Hamilton, but they did inspire popular ballads at the time. John Knox writing about them said,"The ballads of the age did witness which we for modesty's sake omit." Also we have the other lady in waiting hanged for infanticide. This would have greatly excited the scandal mongers of the day
It is likely that an early version of our ballad emerged at this time.
Mary Hamilton was a maid of honour at the court of Catherine the Great. She was executed for killing her baby. The father was widely believed to have been the Tsar Peter. So many parallels to the song can hardly be coincidence.
Clearly some long forgotten balladeer wove all these threads together and produced the hauntingly lovely song that has come down to us.
So you see Guest, it did happen, and it does matter. Poor Mary dying friendless and far from home deserves to have her story sung and the cruel injustice remembered.