Read the documents that I mentioned, the cases were all resized and cleaned before they were weighed so outside dimensions weren't an issue. The problem is that cartridge brass, like all metals, isn't exactly the same, the amount of constituent metals can vary slightly which changes the characteristics of the brass. Also, the thickness of the brass isn't always the same, regardless of whether it's new or used. The area around the web is where you'll find the most variation, sometimes the web is thicker and the taper between the web and the walls is different, these all change the characteristics of the case.
What's confusing to most people, and where this myth started, is the fact that in general terms you can use the weight as a guide to volume changes on a large scale but when you start to drill down to exact weights and volumes there is no direct correlation. In other words, if you want to classify case volumes by creating weight groups of 3 or 4 grain increments and then average the volume changes you will get fairly decent correlation between the two. But if you create weight groups of 1 grain increments the volume wont follow the weight reliably.
A hunter that just wants reasonably consistent ammo can just use cases from the same manufacturer in the same lot number and get reliable results, he doesn't need to compare precise volumes. On the other hand, if you are a long range competition shooter then you'd be better off measuring the volume of every case you load because weighing them wont provide the consistent volume that you need to be produce your precision long range ammo.