I think it is that they don't trust the court to be impartial and fair. After all the UN has countries like Libya on its committee of human rights. Not a great advert for these types of pan national organisations. They can be hijacked for political purposes, i'm sure that some countries would be delighted to try and embarrass the USA with this court, even to the extent of being unjust.
War criminals have been brought to court before without an ICC, just a few years ago a Nazi war criminal was arrested and tried in the UK. Not being in the ICC does not necessarly mean not taking any action against war crimes.