Tom, you are exactly right. There is some proof for your Robert Glenn of Lancaster, however. This is not my line but Marilyn Glenn Szum has all the actual records that can be found to date. She watches this board and will likely respond. My experience is that most of the Glen-Glenn-Glyn names in the PA area in the early and mid 1700's were the Ulster Scots, that is they had come from Scotland much earlier but migrated to northern Ireland. My Glenn ancestor was a John Glenn PA b. 1771 probably in Cumberland County PA. However, in the 1880 census five of his children survived and two said their father was born in PA and two said Ireland. That is how I know at least that his recent roots were Northern Ireland and not Scotland. Your best bet at sorting out fact from fiction is to find a male Glenn from your line and do DNA testing.
Good luck.
Joy