You can't really hold that against him, the Kingdom of Scotland had undergone Normanisation long before he was around. It started under the Dunkelds, and there was plenty of Norman blood in the Dunkeld line before it fell.Robert the Bruce aka Robert Dr Bruis was s Norman.
The idea of a "pure" Scotsman is nonsense.
Before the Dunkelds there was a lot of Norwegian and Anglo-Saxon influence and intermarriage. You'd probably have to go back to the 9th century or so to find something resembling "pure" Pictishness, which, in itself, is a mishmash hodgepodge of various Celtic cultures.