I've only ridden single pivot suspension (Heckler, Morewood), so I can't really comment on "brake jack." All I can say is that any traits inherent to single pivot suspension have never made me feel any loss of control while on the brakes.
As for stiffness, my '05 Heckler is as stiff as it needs to be for trail riding, including aggressive trail/all-mountain/light freeride/whatever you call it these days. The only time I've noticed any rear end flex was riding at Diablo. On particularly rocky downhill trails, I could definitely feel flex in the rear end. But for 99.9% of the riding my Heckler is used for, it's perfect.
The '07's are supposed to be stiffer, so I'd think they would be plenty stiff. (of course, that's just e-speculation from somebody who's never ridden an '07.)