Yes I agree pushing on the ground with knee or any other body part would definitely decrease the downforce on the tires and is a very bad idea indeed.
The thing I am struggling with is when I imagine a rider and motorcycle system in space from rear and the rider pushes with his bottom the left...
Sure maybe they are not right at the limit mid corner but anything they can do to increase the grip even if momentarily so they can pick their bikes up, and I agree that probably doesn't mean that if they didn't do what they did with their body they fall, but if you could increase your tires...
Would throwing your upper body more "in" work as well (or down towards the ground since these usually take place at over 60 degrees of lean)? That is what many of the top guys in MotoGP are doing as I watch their onboard runs. Some even lift their outside leg if they already slid a bit and...
In the case where ground clearence isn't the limiting factor;
Since motorycles are steered using countersteering, a motorcycle cornering at constant max g can achieve any decrease of lean angle (bringing the bike up) by turning harder towards the inside of the turn momentarily, which is not...