By that definition, Stephen F. Austin, a native of Virginia whose father was a native of Connecticut and who was in part educated in Connecticut, would not qualify as a Texan. I do not think a Texan must exclusively be someone of Anglo-Southern descent. You would, for starters, exclude Texans of German, Czech, Polish, Hispanic, and Cajun descent who have lived in the Lone Star State for generations.
My point is that GWB may live in Texas but he is a native of Connecticut, not Texas...and no, SF Austin was a Virginian, not a Texan. Simply moving to Texas doesn't mean your a Texan.