Generally it is mean exactly that.
The judicial system is a branch of governmental authority. Any government on the planet Earth sees the establishment of unauthorize parallel branches of authority as one of the most serious crimes, and people who belong to such bodies face extremely harsh penalties up to physical elimination by the military force.
In reality, it was established by treaty, and 125 countries have chosen to vest authority in it. Originally that list included Israel, the US, and Russia, who supported the establishment of the court but subsequently withdrew when they perceived that being member states would constrain their strategic ambitions.
Also, the jurisdiction of the US does not extend beyond its territory, except in case of war.
reality is more complciated than the simplistic characterization: https://en.wikipedia.org/wiki/United_States_and_the_Internat...
It's very clear that there's a tension between soveriegnty and accountability at work here, with the US seeking to both have its cake and eat it. Many of the objections to the Treaty of Rome stated by US commentators are equally applicable to the Nuremberg tribunals post WW2, for example.