Depends on the gun. I had a Ruger Security Six that wouldn't group .38s into less than 3.5" at 25 off a rest, and that was wadcutters! I'd shoot 1" with a 140 Speer magnum load. I had a M19 Smith that would shoot 2"+ with specials, wadcutters and about an inch and a half with magnums. I got a Rossi M971 that'd shoot 2" groups at 25 with either, pretty decent. Then, I got a Taurus M66. That gun shoots the 140 Speer OR the .38 wadcutter into little sub 1" clusters when I can concentrate enough. The gun is more accurate than me with either load. That's the one I have kept. I have a 3" version of that 66 that is only slightly less accurate. Those Taurus 66s are amazing, most accurate medium frame .357s with either mag OR special that I've ever fired. I also have a 6.5" Blackhawk in .357 that will put .38s into about an inch and a half. Magnums are 1" out of that gun or slightly less. I don't really own that one to shoot .38s from, though. It eats a lot of hot 180 grain XTP hunting loads and my 158 SWC load and darned few .38s. It's a beast, can handle the pounding that would crater a K frame. I hunt some with it and carry it afield on occasion.
So, in general, I don't think this old axiom is necessarily true. It all just depends on the particular gun, I think. It does require an elevation adjustment to switch from one load to another except in my 3" M66 which, for some od reason, shoots just a hair lower with wadcutters than .357s, not enough to mess with the sights over. I have the sights on that Ruger and my other Taurus marked for .38 or .357 elevation for easy reference with the elevation screw.