Ever thought about why you can't "steer away" from a curb, how it appears to "suck you in" when you try? It's because that first, subconscious turn in the wrong direction takes you into the curb edge.
You heard wrong. It's because you can't countersteer, which is the only way to turn a bicycle or motorcycle at speed.
Try it. Get on a bike. Go straight, and pick up speed. Intentionally press the right side of the handlebar. Note which direction the bike is now aiming.