I've never signed on to any agreement with my government, but I'm beholden to the law nevertheless.

I partly agree but largely disagree.  Unless we agree to hand over our right to make our own laws to another body is certain cases, then we should be under no obligation to follow laws we have not signed on to.  I've never read the laws, but I'm assuming that there is no law allowing an international organization to force us to accept an institution like the ICC.  The correct analogy is not "My Government and I" but "My Neighbor and I".  Imagine your neighbor suddenly saying to you, out of the blue, "Hey, pal, your lawn is 3/4s of an inch too long.  Fix it."  You wouldn't take him seriously and would probably tell him, "It's my lawn, jackass.  Piss off."  And you would be right to do so.

Be nice to America. Or we'll bring democracy to your country.