Before I begin, let me express my doubt that Andrew Reid, born about 1650 in Scotland or Ireland, was married to Magdalene McDowell; I think this is a confusion with the Andrew Reid from a much later generation who married Magdalene McDowell in Virginia, daughter of Samuel McDowell and Mary McClung.
That aside, I have been researching the possibility that the mother of this Andrew Reid belonged to the family of Gray of Fowlis. The lands of Knap were part of the barony of Fowlis; I have found that a John Reid possessed Knap and had, maybe among others, sons Gilbert, John, Patrick, James, Andrew, and Robert. This cluster of names is found in the Gray family. The name Robert came into the family via Robert Stewart, father-in-law of the 6th Lord Gray.
Our Andrew Reid is supposed to have been the son of a John Reid. Reports float around the internet of a John Reid being married to an Agnes Gray (often confused, I believe, with a James Reid who married Agnes Gray in Lanarkshire in 1667). The name Agnes is repeated among our Andrew Reid's descendants.
I am unfamiliar with Scottish law and custom, but am interested in the fact that four of the sons of John Reid of Knap purchased a great deal of the lands belonging to William, Master of Gray and his wife Anne, Mistress of Gray. I would think that these Reids, in order to possess Knap, were children of a daughter of William and Anne Gray, or, more likely based on the dates of transactions, a younger sister of Anne.