Interestingly, the rider appears to be a big factor.

Last year I was visiting a friend in Bend, OR and borrowed his bike to do a hilly ride. The bike, (a Specialized something or other, I don't specifically remember) was perhaps a tad small, but fit me OK. Anyway, on a less than 40 mile ride, I got the wobbles not once, but twice, and at very low speeds - 35mph+/-. Moving my weight forward and backward didn't help and with hands loose on the bars and knees pressed against the top bar, I still had to slow to a crawl before they stopped. It was a very odd ride.

My friend is a very serious rider and everything is true and tight on his ride. He stated that he NEVER felt a wobble on this bike and he regularly rides well over 50 mph.

Sometimes the wobbles are a mystery.

Edit:

FWIW, the one time I got the wobbles on my BMC was no mystery. I landed a little crooked after bunny hopping an expansion joint at about 40 mph. An exciting couple of seconds followed. ;-)

note to self: No more bunny hopping north of 40 mph.