A bike that is not moving or moving slowly is inherently unstable - like a pencil on end, it will fall over.

A normal bike moving at typical speeds (within a wide speed range) is stable, and no counter-steering by the rider is necessary. When a bike starts leaning to the left, it starts turning to the left. However, the front wheel will also turn to the left enough to straighten the bike out. This happens with no rider input. How well this works at different speeds can be tuned by changing the steering geometry.

The steering geometry works for the motorcycle too. Gyroscopic forces are pretty strong on a motorcycle with heavy wheels, and they can be felt pretty easily when spinning the rear wheel off road. The bicycle situation is different.

I think that the convict (Doctor) was just trying to make bikes out to be dangerous by using rhetoric (inherently unstable and likely to cause the rider to fall off or hit a small child), so that he would have a reason to want to avoid them. The language seems to plug in to the unpredictable theme. I wonder if his legal team tried that line out on a focus group prior to letting it sail in court. It seems to fail the laugh test to me.