Further to my previous reply. Given that Hugh and Peggynamed their first son Archibald, this increases the chances of Hugh's fathers forename being Archibald, as the Scottish traditional naming pattern dictated so. However by no means everyone followed the tradition.
It may be that someone has seen that there was a Hugh McMillan born in 1812 in Tiree, with fathers name Archibald, and ASSUMED that this must be him. Alternatively, they may well have found evidence which proves that it's definitely him. You would have to ask the person from whom that claim originated where they obtained their source evidence.