Hmmm, my ears were burning and after reading this thread I think some ideas may have been twisted around a bit. I don't know where the original reference to driving technique is but I'll attempt to illustrate my method of "faster through the corners".
Cars always accelerate faster in a straight line. They also stop better in a straight line. The fastest way around a track is taking the corners out of the corners as much as possible because whenever the tires are side loaded, you are scrubbing speed and going slower.
Type 1: The most common 90*ish turn benefits from a late apex where you brake in a straight line, perform a quick turn-in so you can immediately go to the gas as you unwind the wheel. Under ideal conditions you will be at full throttle and unwound at the apex effectively lengthening the straightaway under acceleration. The longer you are on the gas in a straight line, the faster you go around the track.
Type 2: On some corners like a 180* or a banked 160* a type 1 turn is the safe play but a double apex is faster. On a right hand banked 160* I prefer to approach on the far left, turn in early with no braking yet, run a straight line to the top of the bank braking very late and rotating the car quickly in a controlled slide. Once it is pointing to my exit I unwind the wheel as I roll on the gas, being full throttle at the 2nd apex. This cannot work in every corner and it carries more risk if you get it wrong, but it can be very effective because it lengthens the straight both on entry and exit, minimizing side loading the tires, and maximizing time on the throttle in a straight line. Practice this one where there are no walls or obstructions to hit if you get it wrong.
This guy demonstrates both techniques here while keeping the car absolutely at the limit of grip in every corner:
https://www.youtube.com/watch?v=fLCpHnA54cQ