But largely you're right, the story is more complicated. I originally heard it in a non-English interview with some Colonel (OF-5, the rank just below General of brigade).

Personally I am very much against the idea of a democratic nation allowing a private company have a combat strength of an infantry brigade. Definitely too much. (And of course such structures, if they exist, must be penetrated by intelligence, though this is not something you can legislate or even admit).