I think striaght line path is very much as JD describes. If you are constantly accelerating the tip continues to bend. I think the idea is that if at any time you let up on the acceleration or slow down, the tip unbends a bit and you no longer have a straight line path and in fact can pretty easily get a tailing loop.
Although I can cast using Lefty's method I prefer a much shorter stroke with not all that much drift. Under adverse conditions - ie wind, I will use a longer stroke as this helps with the timing. I am a firm beliver in the use of the wrist to give the SUAS - both on the back cast and forward cast. IF you start the cast with the arm comfortably at your side with the tip angling towards the water your elbow is about at a 90 degree angle - to get the tip angling down, the wrist is closed. The back cast is simply accelerating up to a stop with the hand opposite the ear and the thumb pointing straight up - for the thumb to point straight up, your wrist had to go from closed to straight - this is the last thing that happens and just this little snap creates a burst of acceleration that is hard to acheive with just arm motion alone. Once you stop you can drift back as much as you want- this has nothing to do with the back cast but is just setting up the forward cast. No dirft is really needed if your timing is spot on but if you start forward too soon you will not be loading the rod and run out of room on the forward stroke and thus drifting allows some leeway here. The forward cast is a very short stroke - just dropping from the shoulder keeping the elbow bent and the last thing that occurs is you turn over the wrist. IF you stop with the hand just below eye level with the elbow bent, your rod stops at a very high angle and you get a very tight loop. If your rotate the elbow some during the forward cast then turn the wrist over, the rod ends up lower with a wider loop. So at least in the technique I mostly use it is really where the rod tip stops that creates a tight or open loop - the final acceleration using the wrist is the same but rotating the elbow some just before turning over the wrist opens up the loop
Watching Steve R on Mel's Advanced tape really drove home this short stoke on the back cast with little drift. It also drove home a point that during his false casts he stopped high with very tight loops - on his last cast in one sequence he accelerated forward with his arm stright and the rod dropped alot and the loop was much wider on this last cast - so he only got out to around 140 feet!!