Reel, I've shot Remingtons from 1963 vintage to present, some had worse barrels than others which is true of most factory brands. The triggers were another story and I'm assuming you're only inquiring about the model 700. Never heard any report of "bent" barrels. Perhaps a UPS or FedEx bend.
I've heard and read lots of stories about bent barrels. One claims that while cleaning a new rifle on a certified flat surface he noticed light coming from under the barrels edge. Never did explain why he remove the barrel from the action (which would have been necessary to make that observation) or how he accounted for barrel taper, etc.) IMO, most if not all of those stories are BS. Admittedly, a badly produced barrel or whatever part that's being made will sometimes slip through QA techs in a factory environment - it happed in one of my previous jobs where we made electronic controls for the space shuttle and I worked in QA. If you saw how Smith and Wesson corrects cylinder to barrel alignment it would make you cringe. Don't worry about it. You can tune a bent barrel rifle to shoot accurately. It's where the muzzle is pointed when the bullet exits that determines where the bullet ends up.
This reminds me of a story about a guy complaining to a small gun shop owner that the rifle he had bought from the guy had a bent barrel so the shop owner told the fella to bring the rifle in and he would fix it. Upon getting the rifle in his hands the shop owner took the fella complaining to his workshop in the back and proceeded to put the rifle in a vice and went to bend the barrel straight. The fella complaining grabbed his rifle before the shop owner could do anything and left the shop. This same shop owner used to shim scope ring bases if he didn't have the right kind in stock. By the way this is a true story. Thank goodness there is guys out there that know better than to try **** like that these days. I have heard Savage bends their barrels straight, they have them set up on some sort of jig and look down the barrel and if they see a shadow at a certain point in the barrel that's where the pressure is applied to straighten the barrel.
Most factory barrels are still straightened after they are bored because they aren't drilled straight. They use a barrel straightener that is used to Bend the barrel on the outside to straighten the bore. This is/was common practice.
When you place a barrel between centers, it will have run out on the outside of the barrel if it was straightened. there is an expectable amount of run out that varies from different manufactures of custom barrel makers and it normally ranges from .001 to .007. factory barrels may vary up to .050 +. Barrels with run out will lose accuracy the more run out they have because as they heat up the barrel expansion will be different from one side to the other.
Premium custom barrels normally have less than .002 thousandths and many times that is caused by external sanding to remove machine marks. When building a precision rifle, if it has any run out I like to re contour it between centers to bring run out to .000.
A small amount of run out doesn't seem to matter as long as the consecutive shots are held to a minimum and heat is controlled.
So "Bent barrels" could just be the outside because of straightening and not hurt accuracy as long as it wasn't to bad. Most if not all factory barrels will show run out (Look Bent)if placed between centers but as long as the barrel bore is straight you have a chance that it will shoot well.