I was wondering if you had completely lost you head there Guy?!
Some people check a King on the flop, but lots of people also bet it. I for example would almost always bet a king here, because when people raise preflop and check this flop, its rare that they have nothing and just check fold. If they had JT for example you'd expect them to continuation bet such a dry board. So when people check they usually have something half decent, like Ace high, or a pocket pair. So we bet with a KING because they're unlikely to be check folding.
Excellent post.