Uhmmm, I guess you might see it that way. I wouldn't say it meant the Federal term meant higher authority. The Federal Government of the United States, minus 13, or the United States Government, either way, was not the government recognized by the minus 13 so it couldn't be higher. It was just another government trying to run over people. That's what governments do. It's their job. It doesn't make em higher though. Maybe bigger, better funded but not higher. The states in the Confederate States were not under the power of the lawmakers in DC for at least a few years. It was a shot, they took it and it didn't work out. For those few years, there was no "tactic" recognition that the Federal Army was the higher authority. The orders for that Army were not followed by those in the Confederate Army.
All of this "recognition" or not stuff is really just for talking points anyway. The fact is The Army of the Confederate States existed. It went to war with the Army of the United States. With bullets flying and cannonballs smashing stuff, does anyone really not recognize an opposing force? Just wonderin---