It's a very strange myth that closing the bail by turning the handle causes line twist. People who believe this are not visualizing the mechanics of how the line goes on to the spool, and this includes a lot of pros (who are good fishermen but downright lousy at picturing mechanical things). I challenge anyone to describe the mechanism that would cause this. Whether the bail catches the line during the time that the head makes a tiny fraction of a turn or while it's stationary makes no difference (the actual line-engagement happens faster than the blink of an eye, so the motion of the reel head during that moment is minuscule, and don't forget that the head is going to continue that same twisting action during the whole retrieve). I haven't had line get twisted on a spinning reel even a single time in almost 50 years, and until a few years ago I didn't even have modern reels which offered the manual bail-closing option (and by force of habit, I still close the bail on all my new reels by turning the handle, every time). The last time I had the line get twisted was when I was 11 years old and I didn't know better than to turn the handle when a huge fish is pulling drag. Lures that spin when retrieved are the other cause.
As to how you spool your reel with line, I run the line off the factory spool in a non-twist fashion with the spool rotating on an axle of some kind. Yes, that means the line twists going onto the reel one twist for every new lap onto the spool, but it untwists by the same amount as it comes off the spool again when you cast. The idea of having the line come off the factory spool from the side, in a direction that counteracts the rotation of the reel head, makes sense on the face of things, but since the factory spool is always so much larger than the reel spool, it won't ever be possible to get the two twisting actions to cancel each other out. And if you did get it right, the line would be untwisted while on the spool but would take on one twist for every turn while coming off the spool during a cast, and is that what you want, a line that's twisted while it's out there working for you? It's not what I want. I want the line to be free of twists while it's out there working, and I don't care if it's slightly twisted while safely stored on the reel spool. So, letting the line twist one turn per rotation of the head going onto the reel and then to untwist one turn for every wrap of the line coming off while casting works just fine.
Now, if you routinely catch really large fish that pull huge amounts of line against the drag, that's a situation where the line coming off the spool doesn't untwist to counteract the twist that took place while being wound onto the spool in the first place. We've all had fish take out short lengths of line but I've never met a fishermen who catches fish that take out similar lengths of line as the lengths being cast. But if that happened, it would create a line-twist problem before too long. In that case (or in any other case where line twist is unavoidable), dragging a free line behind the boat for a while, then reeling it in, will take care of the problem.
Finally, don't confuse line memory with line twist. They are not the same thing. People who use very stiff mono with persistent memory are likely to have problems that some might interpret as line twist.