The problem is, that a wheel balancing machine does not balance the wheel 'at speed' or while it's in operation on a car.
Just because it is in static balance at 20mph doesn't mean that it will still be sufficiently in balance at 100mph. Most people just take for granted that it does.
The faster it spins, the more critical the balance is and the less it takes to eff it up.
That said, it should be good enough to reach 65mph without an issue unless something was done wrong like...
Wheel balancing machines can be out of calibration, your tires may have tread separating from the carcass, you may have some minimum wage idiot balancing your tires, they may not have the right adapter to mount your wheels on the machine properly, they may not have weights that fit your rim properly, you may have a rim with an imperfection that you can't solve with balancing weights... there is only so much weight you can put on a rim to balance it before the center of the balance point is no longer close enough to where the machine says the weight needs to go.
Need more? All rims have a 'high' spot (yes it is tiny, but big enough), and tires likewise have a high spot and low spot. Most tires worth their salt have color dot markers on these points, and the a good enough balancing machine can map the surface of the rim's lip and match it to the best point on the tire.
If you are THAT concerned with tire balance, find your local Porsche (or similarly high end) dealership and pony up the money for them to do the balance. Their machine is better, their staff are more skilled, and they will tell you if there is something wrong that won't correct. Yes they will look at you funny for bringing a Honda there, just call in advance and make sure they'll look at it.