One thing of note that I just thought of was the fact that when the Book about Dr D Hayes Agnew was written in 1892 that there is more support for the fact that they believed that they descended from the Agnew of Lochnaw family.
The book was written well before "The Book of the Agnews", which was written in 1926.
This lends support for the fact that the family of Captain James Agnew (1711-1770)believed that they were descendants of Agnews of Lochnaw and in the book it was indicated that he descended from Sir Patrick Agnew and Margaret Kennedy.That supports the Royal connection.The Royal Connection was already in the family well before this Agnew-Kennedy marriage but the writer of this book noted that this marrage was a royal connection.
He noted that The marriage between Andrew Agnew and Mary Kennedy took place in 1426 as well.
The main point is that they thought that they were of this family.Where did they get such ideas?I believe that we have evidence that it started with Captain James Agnew, Jr or his Father James.Captain James would have been too young when they left so it must have come from his father.
The book is "History of the Life of D. Hayes Agnew" by Jedidiah Howe Adams.I have it pulled up right now.
Below is the web site where book can be found.Copy and paste the whole thing.