Yes, it's my understanding states are responsible for the actions of their citizens. It's international law so overrides their own country's law in that respect. If a US citizens plans anything against the OST, it is the US government's responsibility to stop them in the first instance. They couldn't get out of that international responsibility by, say, passing a local law to say they are not responsible.
Like quarantine laws. Doesn't get the government out of the need to apply quarantine laws if a private citizen leaves the US or arrives in the US on a private yacht, or parachutes in from an airship or leaves the country in a hot air balloon, still the US government is responsible for making sure they keep the quarantine laws.
If they launch from another country, it doesn't absolve the US from responsibility. If you had say citizens from several different countries, using equipment supplied by another and launched from yet another, all those countries collectively are responsible for making sure they uphold the OST. The more countries get involved, then the more are involved also in making sure you keep to the OST.
In the case of interplanetary protection, then COSPAR meets every two years, and decides on details of interpretation. But the actual enforcing and advising is done by planetary protection officers and the like in the individual countries. So would be like that more generally.
I am not a lawyer so this is just a lay person's understanding of how it works.