Indeed. I like this clip where they show bike steering to the left, without its front wheel ever going to the right side of its original path, by only leaning and no countersteering. https://youtu.be/9cNmUNHSBac?t=445
That's with no rider on the bike. Earlier in the video when he attempts to turn with the device that prevents countersteering, he falls off every time. It seems unlikely that 50M cyclists could easily do this but he could not.
The bicycle and riding style used in the video do not provide a good illustration, I have no idea what he was trying to do as he crashed repeatedly, and he did not seem (or the frame prevented him) to use the ability of his body to lean the bike into the turn, riding naively (which didn't prevent them from talking down as if there is a clear consensus in the field of bicycle dynamics).
At low speeds on e.g. a light MTB stop pedaling, lift your butt off the saddle, lean bike far into desired side balancing your body and handlebars to keep going straight. You have most of what's needed to turn. You may countersteer but your line does not veer into the direction of countersteer, counter to illustrations.
Riding edge of a cliff is not a great idea anyway because balancing a bicycle tends to require countless small adjustments even due to pedaling alone.
You don't just believe the physics. If there is consensus in physics that says you cannot turn a bicycle without measurably turning the opposite way first, feel free to link. It's a ridiculous claim that assumes certain speeds, bicycle type and riding style. I've seen a guy ride a narrow rocky ridge, even jumping from stone to stone where needed (without stepping off the bicycle), was he violating laws of physics or is the world more complex than simplified models of it? Either way, it is just bikeshedding.
Now just imagine the possibilities with a rider on the bike. Being able to dynamically shift weight to either the left or right side of the bike at will! You can even do turns while riding with no hands.
If this were the case, you wouldn't be able to turn while riding with no hands. Yet reality has us out here riding bikes with no hands making turns. https://youtu.be/_SWdCutqSWQ?t=73
That is false, because you can induce a motion of the steering column without using your hands. If you shift your center of gravity around without your hands on the bars, the steering column will do things on its own and you can learn to predict and control that. Not just simply 0shifting the center of gravity in the seat; you can do things if you seize the top bar between your knees.
A steering column which somehow turns right without your hands will induce a countersteer to the left the same way as if you had used your hands.
The video shows the exact opposite of your claim. The bicycle is given an initial push by the experimenter. Its steering is initially pointing a bit to the left. Because of this, it begins falling to the right, and recovers by steering in that direction, away from the guardrail.
The bike seems to be initially leaning to the left, because it was induced into motion that way by the experimenter. Yet in spite of this, it recovers by tilting to the right.
Looks to me like 1. The bike is initially rolling straight with no handlebar angle, and then starts falling over to the left. 2. Due to the mechanic explained in the video, this causes the handlebar to turn left.
If there was a human on that bike wanting to turn, here they would continue leaning, turning, and pedaling in the correct amounts.
But because there's no human to keep their weight leaned to the left, then 3. The left turn of the handlebars causes the road contact points to move to the left of the center of gravity, so that 4. It starts turning right.