Regarding the "violent" pitching.
I have seen (from the jump seat) an A330, fully autopilot coupled, pitch itself down into its own "pitch attitude protection" limit in OP DES. This was due to the captain pulling open descent at Mach .82 at 41,000 feet and descending from a 100-ish knot headwind into a 50-ish knot tailwind through a fairly tight shear layer. The thing just couldn't catch the speed target, as it kept creeping up the tape while the actual airspeed was affected by the tailwind shear.
The vertical rate got to about 7000 FPM (indicator turns yellow) down within a matter of about 10 seconds, and the pitch dropped below 12 degrees. As the plane went thru another shear layer, the pitch touched the green hash marks and started to immediately rise. This of course made the speed drop, causing the airplane to pitch down again, etc etc etc.
The whole process here took less than 20 seconds. It took the operating crew that long to respond to my corrective callout. Why? They were busy looking out the window for traffic to follow, while complying with a descent clearance. The autopilot was so amazingly smooth that they simply did not notice until it was diving like a homesick brick. Nighttime with no moon, no horizon outside to reference.
Both of your comments, in other words are true.
Moral? In normal situations don't pull open descent at FL410 if you are descending into a tailwind / quickly weakening headwind.