Most of the truth behind this theory has to do with combinations of factors (e.g. the guns the round is commonly chambered in, the type of shooting most commonly done with this cartridge, etc.), rather than the specifics of a certain cartridge.
As others have said, there's been A LOT of precision bulls-eye shooting done with .45ACP. So it has a reputation for being very accurate. Well, duh. Put that much work, for that many years, into squeezing groups down and you'll have a very accurate cartridge. Doesn't mean that the .45 is inherently more accurate than 9mm or .38 or 10mm or anything else. The road is just well-trod.
Now, in the upper tier of benchrest rifle shooting there are very worthy debates about the inherent properties of the various cartridges used for that sport. Those guys are really talking about almost immesurable differences that could/might produce a win, and they're trying to isolate every piece of human influence out of the equation so that mechanical accuracy can shine through.
That really doesn't apply to service handguns and the cartridges they shoot.