Well, if they want to be pedantic about it, they are not correct. In the USA, per 21 CFR 133.165, the standards of identity define what may be called Parmesan. And pretty sure (nobody has done the lab work) your make would yield the appropriate moisture and fat levels. Your make process also follows the acceptable identity standards.
In Europe, the DOP protection is extended ONLY to "Parmigiano-Reggiano", and NOT "Parmesan".
So, sir, your cheese is a true parmesan per US standards, where you live. It is not, however, parmigiano-reggiano, nor is it Grana Padano (another DOP cheese). Or to be more exact it is a Parmesan, which is a grana-family cheese.
The point of DOP protection is to extend protection to true and legitimate products whose authenticity can be verified. You can't just extend DOP protection to names that are in common use, like Parmesan.