Jason Kenney may have missed it, but Lyndon Johnson's famous comment about how certain people weren't up to walking and chewing gum at the same time was an observation about their lack of intelligence, not their ability to get away with saying contradictory things at the same time.
Alberta's premier is said to be a pretty bright guy, so presumably he understands what the Democrat from Texas had in mind when he pithily observed that Republican congressman Gerald Ford was "so dumb he can't fart and chew gum at the same time."