On the family tree on Ancestry they have Alexander living around Lanark, but moving between Bothwell and Stirlng several times.....I can only assume one of the connections is wrong, the parents were in a location other than home when the baby was born. Looking on map the two locations are not far apart, and it appears the whole family had connections in both places.
The tree the other person has built has lots of scripts and documents from various sources, including residency documents