If the police tow it, I'm sure the owner of the car would have to pay the fees. If the property owner tows it, I'm pretty sure they wouldn't (although it may vary by state). At least in Toronto, you are allowed to tow a car from your property, but not charge the owner for the tow [1].
San Diego typically the owner of the vehicle pays the fees when its towed from private property not the owner of the property. It seems the lawsuit is based around considering the fees are higher than legally allowed.
It says if they have posted signs with the law, they can contact the police to issue a ticket (and tow, presumably). The formatting is a bit messed up, but you are required to both have the signs, and contact the police, you can't just tow it without calling the police, and require the owner to pay for the tow.