The issue of airport proprietors vis a vis aircraft noise has been clear since 1962 when the United States Supreme Court ruled that proprietors are libel for damages by noise from aircraft. (Griggs v. Allegheny County, 369 U. S. 84)
According to FAA.gov, "The role of the proprietor described by the Court remains the same today."
In 1976, the US District Court for the Northern District of California reiterated that if a local government is the proprietor of an airport, it can limit the noise from aircraft using that airport. (National Aviation v. City of Hayward, 418 F.Supp. 417, ND Cal., 1976).
Following are more government sources substantiating that airport proprietors (in this case, the City and County of San Francisco) are legally responsible for the effect of aircraft noise on the surrounding community.