The Scout camp in San Diego that is being referenced here is probably the one in Balboa Park. This is public parkland that the BSA leases from the city. The ACLU has brought suit to get the lease cancelled and get the BSA thrown off of the land, on the basis that the BSA's membeship policies keep the public from using the land.
Of course, I doubt they'll support reimbursing the BSA the millions they've spent on improving the land, nor do they consider that the public is allowed to use the land numerous times during they year when summer camp is not in session, and use the facilities that the local Council has built.
Until the lease is voided, it's private, though. The holder of a lease of public land has just as much right to keep the public out as someone who owns the land.