Cary Fowler clarifies matters:
Just to be clear, Svalbard does NOT impose SMTA requirements on countries that deposit. (Cases in point: the 69,000+ samples deposited by the U.S. and the 2,000+ deposited by the Seed Savers Exchange, an NGO.)
Treaty Parties and non-Parties alike are making use of the Seed Vault and use by non-Parties does not change the legal status of those deposits at all.
You can believe that if you want to.