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Yes, the accepted explanation is the one cited by you and Marc, but the distribution is problematic.
It appears that the word pilgrim may not be a literal description. Deor (Deoraih, Dewar) was, in some instances at least, a religious office. The Dewar was the keeper of the relic of a saint, usually connected to a particular clan. His function was to take the relic to any gathering or ceremony where its presence was required. So his travelling around the country on a holy mission resulted in his being called 'pilgrim'.
In the Highlands the name Macandeor became Dewar (actually a Lowland Scottish place name). The Dewar of Glendochart, in Perthshire, was the keeper of the crozier of St. Fillan.