That's because, to INITIATE a lean condition on a motorcycle, and to do it quickly and accurately, you have to countersteer. Especially evident in the video when the riders make quick transitions from left to right, right to left. THAT takes an assertive countersteer effort.
Now, when the bike is already leaned over to full lock, countersteer action at the handgrips is clearly limited. At that point the minimum radius the bike can manuever is mostly due to the lean angle and steering head angle already established and the speed of the bike.
Can't say I have done it to know for certain. But say the bike is at a near full lean left, slow speed so the handlebar is TURNED full left against the stop. Countersteering input on the left (down) grip would actually turn the fork away from full lock. In some cases of riding, a regular steering input is needed to make the bike stand up quickly. If the fork is already at full lock left, there is no additional steer angle possible to make the bike stand up. But I bet some front wheel brake will make the bike stand up at that point.
When life throws you a curve,.....lean into it!
42+ year rider, 22+ year MSF Coach, Street, Dirt, Ice, ride em all!