Also using Blackwater mercenaries so they could just brush any of their deaths under the rug as they typically didn't use Americans for dangerous and unprotected jobs.
Also there was a point when Blackwater boasted that they could deploy a light brigade (~3k troops) anywhere in the world, people in the Pentagon figured it out and very quickly killed that org. Compare with Prigozhin and his adventures, just for reference he had more than 10k soldiers under his command, on heavy equipment (arty, tanks, ifvs), permission to illegally recruit from prisons, he even had air defence like Pantsirs, the motherfuckers even tried to get nuclear backpacks (man-portable nuclear bombs) from a storage site near Voronezh.
I think those entities are being tolerated and even welcome, as long as they don't exceed some potentially threatening size.
That... didn't happen.
Blackwater went through several reorgs, rebranding, and acquisitions, initially starting with at least superficially deemphasizing security in favor of other functions because of “business risk” just after the Nisour Massacre, but (as Constellis Holdings) is still doing the things it did before, notably as part of the Saudi intervention in Yemen.
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).
Also pitched a plan to the pentagon about privatizing their presence in Afghanistan and extracting their natural resources to pay for it. https://www.militarytimes.com/news/your-military/2018/09/05/... (didn't vet this source)