Cool. So generally, I guess it all depends on the type of treaty and the type of jurisdiction a country or international tribunal claims to have to be able to try US citizens/USA for violating a treaty. International law is very confusing.
I still disagree, although it’s somewhat of a technicality really between approving and actual ratification. In theory, the Senate could approve, but the President never ratifies. If you scroll further down that link it states:
"The Senate, itself, does not ratify treaties–actual ratification only takes place when the instruments of ratification are formally exchanged between the parties. When a treaty is submitted to the Senate for approval, it has several options for action…The president and the other countries involved must then decide whether to accept the conditions and changes in the legislation, renegotiate the provisions, or abandon the treaty…Most treaties submitted to the Senate have received its advice and consent to ratification, and the ratification has subsequently been signed and deposited in the National Archives by the president."
Interesting. My bad. It’s a subtle but important distinction. The President or his people agree to a treaty. The senate approves with or without modifications. The president and his people then either ratify (exchange the final docs) or not.