That is true, but that "same place" is only a few feet in front of the gun! At least, that is what I have found whenever I checked the regulation on an O/U that shot both barrels to the same spot at 30 yards. It is actually quite stunning to see the first time you do it, and it makes you appreciate how hard it is for O/U manufacturers to get it right. I'm sure the first guy to ever solder two barrels together thot if he could just get them looking at the same spot after solder cooled they would work great. Wrong! Those barrels would have shot 3 feet apart! It must have something to do with the recoil. All I know is it must have taken a lot of trial and error to figure out exactly where the two POA's must converge in order to be correct in the field, and then there is the issue of getting the rib to point at the spot where the two barrels pattern. And then the fact that a gun is not going to recoil against a big, solid shoulder the same way it recoils against a lightweight, soft one.
This problem is exactly why K80's and the Rem. 3200 they were modeled after come/came with front hangers that can be changed out, slightly bending the muzzles apart or together to correct any regulation issue. Obviously there is a limit on this, because the barrels are soldered together back at the breech end, but generally a slight correction is all that is needed.
With any other O/U (and I have owned quite a few) my RULE NO. 1 has been, if at all possible test its regulation on the pattern plate (or on clays laid on a berm, something!) before buying. Obviously, not possible to do on a brand new gun. There I recommend avoiding "value" brands/models and sticking with ones known to *usually* be correct. Japanese- (Kodensha-)made Winchesters were *usually* on or very close, as were Miroku-made Brownings. But I seemed to be a little snake-bit with SKB's. A Perazzi with minimal engraving and plain wood is still pretty expensive, and for a very good reason.
RULE NO. 2 is, if you already own the gun and most of your pheasants are coming down dead,
don't ever take that gun anywhere near a pattern-plate.
What jk80 says is spot on, but for shooting flying targets only. Turkey hunters use "turkey" (X-Full or tighter) chokes and then slowly and carefully aim at the bird's head.
An O/U with a Red-Dot on it should still print both barrels to the same spot, or be no more than an inch or two off. Certainly not 14. That is not going to be fixed by removing the Red-Dot.
Yes, you can frequently change the POI by using a different (screw-in) choke and/or load, but you are not going to correct a 14" disparity. Maybe 6".
RULE NO. 3: Except for turkey hunting, do not assume that where a shotgun (any shotgun) prints on the pattern-board ("high," "low," "left," etc.) is where it is going to be when you are shooting flying. I have fitted many guns to many shooters over the years and I learned long ago to go by where they are shooting flying, not by where they shoot on the pattern-board, because they will not be the same place.
Shooting the way jk80 said, get someone who has enough shotgun coaching experience (and it usually takes a TON) that they can see where you are missing when you shoot flying. When they tell you you are consistently high, low, left, etc., and by how much, then adjust your stock accordingly.
And, yes, it is tricky to know how much to change the stock to correct for your being "X-inches low at 20 yards." A very good gun-fitter will be able to tell you, but those are pretty rare. In fact, after being one for several years I finally concluded they do not exist!

Best advice: buy an O/U with an adjustable comb (or have one installed), or go with one of the semi-auto's that comes with swappable shims between the action and the stock that allow you to change cast and drop, and begin your journey of experimentation and enlightenment.
Yes, jk80, a "custom stock" can be wonderful. But I have also seen very highly regarded fitters get it very, very wrong, so the customer came home with a beautiful, expensive gun with a beautiful, expensive piece of newly carved wood on it . . . that did not fit him.
No problem if you are rich -- you just sell it and start all over again.
Then there is the problem of our gun-fit changing as you age, gain or lose weight, or simply gain experience shooting. Being able to easily change it any time you want is hard to argue with.