I don't think you "tilt" your head in cte, you "poke it out." If you're proficient at doing so, you can come down on the shot correctly and it is pretty much "disguised." In other words you came down correctly and don't have to make adjustments at the table. The "poke out" doesn't only belong to CTE, it's about getting your eyes in the correct position so you're clearly seeing the shot picture. The entire point of the "poking your head out" is to show you what it does and train you to come down into that head position already. If you know you need to "poke left" you come down that way on the shot line. I know it sounds weird, but you're on a dead end if you think head shift will discredit or prove someone is using CTE. I've been doing it since before I learned the very basic CTE and still do it even though I'm not currently using CTE.