Blue Cod certainly do that, they destroyed 3 ledger rigs before I decided just to strayline when I was fishing Titirangi over Easter. I always fish with a light-moderate drag so fish might react differently when there is no drag at all.
edit: Using a piece of tubing over the dropper loop can help prevent them twisting the line.
In the past when I have been battling a stubborn ray or shark I have returned the rod to the stand to attend to other rods which have fish or would get in the way. The first fish have always cooperated for me….