I may have not explained it well. I'm on the same page as you on pivoting. It's not BHE, it's doing the same thing as pivoting. Without the pivot you aim further away and let the deflection carry the ball over to where it needs to be. With the pivot the deflection is baked in and you can aim where you are aiming. Either way works. You're still canceling the effects of deflection, one by a pivot, one by offsetting the aim point. On said break scenario, I aim to hit the second ball dead center, or in other words the edge of the head ball. No pivot, but simply using the stick to deflect/throw the CB into the center of the head ball.
In the break scenario you're actually aiming straight on dead center at the second ball, but deflection (depending on your stick, this is for my stick) will throw the CB on line to strike the head ball center. You have to adjust where you aim based on the stick. With a pivot and the CTE aim perception, the pivot is canceling the deflection. I'm sure you know that the pivot distance is somewhat "do what works and adjust for your stick" in the book. The reason is because all shafts deflect differently. Stan gives us a range to try with the deflection, but each shaft will be a tad different. This isn't a flaw, it's just adjusting for your personal stick. With a LD shaft I'm almost certain the pivot will be smaller than with a standard maple shaft.
One strength of the pivot in CTE is that it kind of takes some of the guess work out of it. You aim where it says and pivot where it says and it works. With other methods, the deflection aspect isn't addressed other than to say it's a thing and you have to account for it. After enough play with the same stick you don't have to think about it, you've hit enough balls for the "feel" to be there.
The good thing about using the same stick for decades is that much of the calculation comes automatically, we call it feel, and I don't know a better way to describe it. It's not some magical thing or some wishy washy thing, just intimate familiarity with the stick you're using. You can adjust for different table conditions. You do so by feel and experience in dealing with different conditions. If a table banks short, you know what to do. If a cloth is slow, or there is a roll off, you know how to adapt and adjust. Your stick is the same always so the adjustment is done without conscious effort, it's the default.