TUC went to great lengths to explain that he wanted others -- not himself -- to merely exaggerate, omit, etc.
I don't know if Vulcans can't lie, or most often choose not to. If it's just a myth, it would be very useful for Vulcans to further it. Anyway, he's only half-Vulcan.
I don't think the ability to lie would be genetic. More than likely the Vulcan aversion to lying would be cultural and learned. Spock is culturally a Vulcan.
Spock and other Vulcans have lied, most notably Tuvok who work undercover in the Maquis.