This is the US Code regarding Destructive Devices:
Release date: 2005-08-31
TITLE 26 > Subtitle E > CHAPTER 53 > Subchapter B > PART 1 > § 5845
Definitions
(f) Destructive device
The term “destructive device” means
(1) any explosive, incendiary, or poison gas
(A) bomb,
(B) grenade,
(C) rocket having a propellent charge of more than four ounces,
(D) missile having an explosive or incendiary charge of more than one-quarter ounce,
(E) mine, or
(F) similar device;
An individual CAN own a Destructive Device (a 40mm M79 HE round for example) but a Form 4 has to be approved and a $200 transfer tax paid for EACH round. If it's actually fired, there's even MORE paperwork required to account for it.
I may be wrong but I would certainly think that explosive cannon and mortar shells would fall under either A or B.
It would be extremely interesting to know what was actually being fired and how it was done so as not to incur the wrath of the ATF guys.