A "blind pig" has no such assurances. Even experienced collectors can get taken if they aren't careful. Especially when it comes to higher value graded guns, some of the restorations can absolutely approach or equal original finishes. But work like that doesn't come cheap either, so is less likely in lesser value guns. And there are guns that have been sold as restorations by the better restoration smiths such as Dewey Vicknair or Doug Turnbull that later get passed off as closet queen originals. You simply have to learn to spot the subtle and not so subtle signs of restorations or refreshing. I certainly have been burned by excessive exuberance and rushing into a purchase without doing all of my homework. It is part of the game, and part of the challenge of gun collecting.
Parkers and Foxes are obviously more tempting for unscrupulous sellers to restore or refresh in order to maximize their profits because of the greater value and demand for them. Refreshing is more common than restoration because a lot of that is done by amateurs and hobbyists. Just look at the number of photos of re-blued barrels you see on this one website in a year. Does anyone think for a moment that some of them aren't getting back into circulation? Look at the long discussions there have been here simply recounting how to verify if barrels have been cut, or had chokes honed, or chambers altered. How about the many discussions of what type of case colors are proper for this gun or that? All of those little details go into defining "unmolested" original collector condition. But if you can detect "unmolested" condition in the other brands you mentioned, there is no difference with a Parker or Fox. A good place to start with the Parkers is to get a copy of the Parker Shotgun Identification and Serialization book so you can at least verify original configuration.
Other than that, there is only verifiable provenance such as absolutely knowing that a very nice or pristine specimen was in the same family, lightly used, and well cared for, from the time it was brand new. As time passes, that gets harder and harder too. Just look at some of the dishonesty you see even when there is no money involved.
