In the years I've owned cars, I've seen the following causes of wheel "shimmying".
Bent rim. (from hitting a curb; hard)
missing wheel weight
bad tire (obvious bowing in one part); broken belt
excessive buildup of snow/ice
excessive buildup of dried mud
I would expect that Toyota would find these, but who knows.
You could got for a "second opinion" at another shop.
Also, are you actually Toyota to take your car out and exceed the speed limit? Horrors!
