Have you tried contacting the Clan Blair archivist?
'The Surnames of Scotland' says that Blair is of territorial origin from one or more of the places of the name.
The origin of the place name is from Gaelic 'blar' which has a lot of meanings including a piece of ground or a battlefield so there are plenty to choose from.
IIRC Balthayock and somewhere near Blairgowrie were also seats of Blair families in Perthshire.
BTW never trust anything you find online unless it's an image of an original document. In particular don't trust online trees - use them as a pointer and confirm every step from originals. You cannot always know whether an online tree has been carefully researched or is a blend of fantasy and wishful thinking. And just because An****y or any other commercial web site has hundreds of trees saying the same thing means nothing, because people find a tree online and attach it to their own without checking, and over time every error is repeated dozens or hundreds of times.