You are right, this seems to be an intepretation of 523 US 767 (1998), a Supreme Court ruling on the boundaries of Ellis Island, applied broadly to Liberty Island.
In that case, the court looked at an 1834 NJ-NY Compact (US Statues at Large, Volume 4, Page 708) that says: "The state of New York shall retain its present jurisdiction of and over Bedlow’s and Ellis’s islands;" interpreting NY's "present jurisdiction" specific to Ellis Island as its low-tide shoreline in 1838, not the landfill that later expanded the island.
The last editor applied the court's reasoning to Liberty Island (was Bedloe/Bedlow), moving its boundary to the 1838 low-tide shoreline as well.
The issue with this is that the Supreme Court only ruled on the boundaries of Ellis Island, not Liberty Island, in 1998. The court themselves didn't apply the same interpretation to Liberty Island. 
So I'm thinking, without any legal action since the 1980s or clarification otherwise, the 1838 Compact still holds - giving NY basically de-facto jurisdiction over all of Liberty Island? I also can't find anything that says there's been any recent legal challenges to this either.