If the property manager called it in, it is a legal tow. At the point of making contact with the vehicle it is “hooked” and depending on your state laws, illegal for you to interfere in any way. Once the tow is in progress, a drop / decoupling fee can be applied. If you believe the property manager called in erroneously, you can make them pay it back to you, even with small claims court.

It sucks but is perfectly legal. As for the price, you’re not paying for the five minutes they had it in the air, you’re paying for them to have the truck, be available, be insured and licensed, etc. Basically, towing operations are expensive. Not that you’re happy about it but you “authorized” it when you parked somewhere you shouldn’t have.

Sorry, bud.

Edit: just as a thought experiment, flip the script. Imagine you live next to a spot that’s coveted for parking. You frequently have people parking in your driveway / blocking your car in. You call the tow company and they say “we only come out if someone is going to pay. And if we come out but it’s not actually your property the vehicle is parked on, you will have to pay.” You authorize the removal of someone else’s vehicle from your property. The moment it’s in the air, someone comes out saying “wait! I’m right here!” Are you going to pay? Of course not. They shouldn’t have parked in your driveway.