That is correct! But the city does own the spot, and it has rules about parking on it. Those rules apply equally against everyone, in principle. But they will never be enforced spontaneously. Someone has to complain, with some valid basis. It exists for these kinds of nuisance situations.
The city is very sympathetic to the concept that some uses of city property (in principle available for use to everyone and anyone) may be annoying to nearby residents.
For instance, some residential streets that are close to transportation amenities or shoppping/business areas have permit-only parking. Only people who can provide proof of residency on a specific street can get a permit to park there; anyone else is in violation, subject to ticketing and towing.