Head movement with Jab?

[Bomp]

I have a question concerning head movement with the Jab. With professional boxing, I notice that most boxers lean their head off to the right when and pivot with their hip when they Jab, like this:

http://www.youtube.com/watch?v=IBnBcGst5CI

I understand that it adds power, but to me, it seems that it leaves you pretty open for a Cross. It also would seem that it takes longer to throw a Cross if you are doing a weight shift with a Jab as opposed to a "straight" Jab and a Cross. Sounds confusing, so here is a video of a straight 1-2 with no hip twists or head movement:

http://www.youtube.com/watch?v=PO4oa6DbrI8

Thoughts?

There are different uses for the jab, and some are illustrated in the top video. Some times the boxer (Larry does it in the vid) reaches a little more and his weight ends on his left foot (often while circling), he does this to disrupt his opponent while moving into a better position and angle. But when used as a set up for the 1-2 they add a hip twist to shift the weight onto the right to come back with a powerful right, if you throw a right when your weight is already on the left foot then it'll only be an arm punch.

I also agree with chris that the twist makes it harder to counter.