My guess: All the above. Weight transfers forward under hard braking as the softly sprung forks collapse. The rear wheel unloads, the shock can't keep up, leading to momentary locking up and chatter you experience.
A riding class could help you figure out how to be smoother on the brakes before a skid on the street cuts a ride short with a fall. It's just technique and practice, practice, practice. Hang in there!
As an instructor buddy once told me, "Don't worry about going so fast at first. Concentrate on being smoooooth. Get that down and you'll be surprised how fast you're going."
I used to have issues with my rear brake locking up way too easily on my Ninja. I installed cheap organic brakes (ebay) and I removed some of the surface area off the brake pads with a grinder so they would grab less (i.e if organic areas of pads are 2" long by 1" wide I grind them so they are 1.5" long by 1" wide making them only 75% effective) , and I also adjusted the brake pedal so I had to push it further to get the brakes to engage. It was much better after these modifications. I also considered shortening the brake pedal and replacing the banjo with one that was more restrictive to allow less fluid to flow through it under force. I haven't had any issues with the rear brake on the FZ9 though, but having 35lbs of ballast (Cecil and his box) directly over the rear wheel probably helps too.
you're probably locking up the rear. i found the stock sintered rear pads to have too much initial bite, so i installed a set of ebc organics (fa174) and they're much more to my liking. i use my rear brake as an ultra fine throttle control in turns, and in low speed maneuvers. the difference in control between the stock pads and ebc organics is like the difference between the stock '14 09's throttle maps and a reflashed ecu.
but it will depend on your own riding style and how you use your rear brakes. some guys don't touch their rear brake at all.
Man, this is the first bike I've ever had where the rear brake didn't lock up easily. My ninja 250 did it all the time even under normal braking, and my dad's Versys does it under hard braking. Have yet to lock it up on the 09, even when practicing panic stops
Had my first "shudder" this weekend.. The first time it happened I almost lost control, then I did it on purpose a few more times to try understand what was happening, and can repeatedly recreate the effect.
Taking another bike out at the same speed and same braking I could not recreate the effect.
I think its traction and braking , compounded by poor rebound setting.. pick you cornering speed more carefully.