Straightening is quite an interesting subject and most heat treaters that quench and temper bar steel (such as used in rifle barrels) used to do it using machines that required operator skill. Some operators never get that skill and "overbend" the bar (barrel) requiring overbending to get it back. I've watched one of our heat treater's operators just mutilate one of our shafts trying to get it straight.
Fortunately there is new automatic straighteners that do not require operators. They measure the runout and get the high point up to the press. The press comes down the exact amount needed to straighten the barrel when the pressure is released. I'm sure some of the rifle makers use these and some do not. We would only allow one "reverse bend" if the initial press was too much. Otherwise it weakens the shaft (barrel).
Maybe more then anyone wants to know about straightening but I was charged with solving this problem once (now retired).