By getting into my Esquif Prelude recently, it was time to question boat tilt once more. Some way or another that boat managed to tip me over to the site I was tilting. So there must be something wrong... . I also knew that something was still wrong because I still didn't get a good grasp on my roll. Yes of course, I do roll my viper11, but fail it with the prelude.

You cannot lift the leg you're standing on

What's in the name, stand on one leg, and try to lift the knee of that leg. It simply won't work.  In a canoe you can suffer the same problem, you push down on one knee. If you're not careful, you start leaning on that knee, like standing on the one leg. And then you cannot lift that knee anymore to equalize the boat tilt. It's like getting in a very light bell-buoy lean, or pushing the gunwale.

Equal pressure on both legs

That's the clue of boat tilt, keep equal pressure on both knees, then you can lift or push if you need extreme compensation. Theory is easy, but how does one do it: you have to work your hips. Your body is an upright upper body, a loose axe in the lower back, and hips that can tilt from one side to the other. If you put an imaginary bar on you hip bones, that bar should always be parallel to the thwarts of your boat.  By working with your hips, you can maintain an equal pressure on both knees, you're balanced. If water pulls you out of balance, then you can counter that action by pushing and pulling to move your balance in the other direction. But only in very rare situations, if hip movement is not enough.

What about push one knee, pull the other?

I think the push one knee and pull the other knee might have to do with an incomplete understanding (not claiming I have a complete understanding!) of how body movement works.

First of all, you can pull up one knee and push down the other without too much hip movement. Have a look at the person riding a bike in front of you, they are actually doing that. No, you should not watch the pro-racers, you'll see they move their hips quite actively to add extra power to the movement, out of the hips!

Secondly pulling your leg over 90° with your upper body is a hard job to do. There is no direct muscle connection that can pull very strongly to pull that leg higher. It can be done, sure, plenty of people can do it, but very few can add power to it.

At last it has to do with how people move. For every move there are muscles that initiate the move and other that support or follow the move. The pushing and pulling might be right for many people to result in working with the hips, but it wasn't the case for me.
The movement one wants to reach is moving the hips as described above. How you reach that movement is another story: push-pull with the knees, hip-muscles, ventral-muscles, whatever muscle that initiates the movement. The others can be used to support that movement.

Compare boat tilt with torso rotation: you don't say bring forward one shoulder bring back the other, no mostly it's just explained with torso rotation and you can focus on improving that rotation by paying attention to what your shoulders do. But the main topic is: torso rotation.

But like I said, this is my interpretation. Most books and videos talk about tilt and knee-motion. If it doesn't work for you, think about tilt differently, think about what you really want to reach: move with the hips. Then  you can figure out what for you the best way is to initiate that move.