Those records were apparently done during the Sancto de Claro Society era and they simply recorded anything they had ever heard. I do not know about the pre-American material but the American material is mostly errors.
I am doing oral histories with several people in their 90s right now and unable to do any of my own research but can respond to some of the material:
John Sinkler who was in Exeter, New Hampshire arrived in Boston, Mass. on 24 February 1652 aboard "The Sarah & John". I have when he went to NH but would have to dig it up.
The Robert Sinclair in New York died in New York. I recall that he did have at least one daughter but no sons - hence the Sinclair name was not carried down. I have his biography somewhere in this morass I call an office.
I do not know about Robert Sinclair, son of John of NH, but his record will be in Morrison's book.
I do not know about William Sinclair in Mass.
The John Sinclair of Fauquier County, Virginia is a brother to our Wayman and was BORN ca. 1707-1711. He was the son of Alexander. Look in your hardbound copy of my book and his record is there.
The earliest American date found for Arthur of Surry County is 1766 when he married his second wife (mother of son Arthur). The 1747 date is from ENGLISH shipping records. I do think he was in America before 1766 but that is not yet proven to my knowledge. It is also possible that he had children by his first wife which is rather a mystery.
John Sinclair who lived near Leesburg, Virginia was not a political exile. He was the documented son of Amos Sinclair and his wife Mrs. Margaret Hawling Sinclair. A large number of descendants are working on that line.
The material on Peter may or may not be correct. I do know that he settled in New Jersey and there are a number of people working on that branch also.
Hope no one takes offense at this correction but I know how very difficult it is to correct an error once it has spread. I ought to know, I've made my share!
I do think it is important for you to put this out though, as there were many members of the Society who undoubtedly copied the same errors over and over and hopefully we can all share and correctly document the lines.