The USAF is not subject to (most) FAA regulations. As far as I know this also extends to training: the USAF does not follow either of the FAA’s Part 61 or 141 flight training syllabi. So bringing up parts 61 and 141 doesn’t really refute the parent’s point.

Regardless, as a civilian, you do have to pass a written multiple-choice test on flying theory before you can solo. Any time you spend in the cockpit before passing that test will be under the supervision of a Certified Flight Instructor (CFI), in a plane with dual controls, and you are not acting a pilot-in-command.

So, although the parent may be slightly over-focused on the USAF way, I think it is fair to say that for any type of pilot training in the USA, you do have to complete academic ground training (including passing a formal written test) before you are truly “given the controls”.