I'm pretty sure he's a bit wrong on the first part.
Almost all of space is very close to being a vacuum so you won't freeze at all quickly despite the technically very low temperature. There's just not enough matter at that temperature to have a significant cooling effect. With conduction and convection pretty much ruled out, the only route for bodyheat loss is radiation and a human body doesn't radiate heat very much at all (too small, too cool). It's nothing at all like having a lump of dry ice on your back, which would freeze you extremely quckly due to conduction.
I'm not so certain about 250C temperatures on the side facing the sun. If you were close enough, sure. But how close is "close enough" in this context?
Also, I think that if you were uprotected and close enough to a star for the temperature to be a problem, the other forms of radiation that he didn't mention at all would also be a problem.
But I think the biggest problem would be the lack of air. With no air and no air pressure, you're going to be completely unconscious in seconds and dead in at most a couple of minutes and probably less. The bends won't be a problem because you'll be dead before it would be. The most pressing problem with your lungs would be them over-inflating, not being "sucked flat". Gases expand a lot if the pressure is reduced to zero. Surface liquid would boil at surface body temperature due to the lack of pressure, but you'd be dead from anoxia before that became a problem. Basically, anoxia would kill you before anything else would with the possible exception of massive internal injury if you were holding your breath and your already fully expanded lungs were wrecked by the sudden expansion of the air in them.