I think if you brought your original argument to a court you would get beat by a first year law student. I do not think a coin struck by a mint employee at the mint while using official dies, planchets, equipment, and paid employees can fall under the definition of counterfeit.
If the employee struck the coin and let it go into the struck coin hopper and it went through all the steps and was released into general population then you would likely lose the argument of using government property for personal gain.
I expect your conversation will not accomplish much beyond making you feel proud of yourself. In a court of law it is not what is true, nor what is right, but what can be proven.