The USTA got the land in 1977, because the Singer Bowl (stadium on the site since the 1964 World Fair) was not being used. They signed expansion contract with the city as Dinkins was on his way out of office in 1993.Little to young for this but I believe a big player in the USTA receiving that land was Mayor Dinkins and his love for the sport. Can't see DeBlasio doing the same for us.
The tennis center is also considered public and open to the public 11 months out of the year. They pay the city something like 2+ million a year depending on US Open attendence.
Totally correct on the public use and money part as well.