You're exactly right. However, the ATF doesn't appear to pay as much attention to the actual bore diameter as they do the name of the cartridge.

"Category I - Firearms" are those "firearms to caliber .50 inclusive."
"Category II - Artillery Projectors" are "guns over caliber .50..."

These and other weapons are all defined in "The United States Munitions List."

Also look at "The National Firarms Act" Title 26, United States Code.
Chapter 53
5845 Definitions

(f) Destructive device. -- The term "destructive device" means... (2) any type of weapon by whatever name known which will, or which may be readily converted to, expel a projectile by the action of an explosive or other propellant, the barrel or barrels of which have a bore of more than one-half inch in diameter, except a shotgun or shotgun shell which the Secretary finds is generally recognized as particularly suitable for sporting purposes;

Respectively, they refrence ".50" and "one-half inch". So why is it that a 50 BMG (.510), 500 Jeffery (.510) and 505 Gibbs (.505) are considered sporting cartridges? I have not been able to find the answer to that. But it's clear in reading the law that a "gun over caliber .50" or one with a "bore of more than one-half inch in diamter" are classified as "artillery projectors" and/or destructive devices and are NFA weapons (unless you receive an ATF exemption letter denoting your cartridge as for "sporting puposes".

I do have a letter from the ATF stating that double rifles are not subject to the classification of the NFA.