There is no misconnotation on my end, I can't help it that definitionof mercenary and your perception of one are two different things. Blackwater might not be bound to only do the USAs bidding, but they still don't represent anyone else so they are not mercs. Even if they were hired by an ally government like UK or Israel they still wouldn't be mercenaries since they are still fighting for the same side.
That would still mean they are mercenaries, they are fighting for money, i mean you could say they are part mercs because they won't go fight for some random non nato country, but will fight for any nato country.