Especially if you consider that George Bush designated the trench a National Monument.
What Obama is doing here is asserting the 200 nautical mile Exclusive Economic Zone(EEZ).
With the Magnussan Act in the mid 70's, the US claimed the 200 nautical mile EEZ for the purpose of commercial fishing. Then, a few years later, the UN Law of the Sea Treaty granted a 200 nautical mile EEZ to all nations for all commercial purposes.
Reagan didn't sign LOST but he issued a proclamation asserting the US's right to the LOST 200 mile EEZ.
