I'm guessing the posted sign said permit parking or resident parking either way she would not have been as you say legitately using it. If it cannot be determined the car belongs to someone living there than it's shouldn't be parked there if there were no signs then the car wouldn't have been towed. So to answer your question pay the bill and learn to pay attention to warning signs before parking. Who knows if enough people actually obeyed the rules when they parked you might put tow companies out of business.
If you can’t determine if someone lives there or not, you probably should not immediately opt for towing them. That’s a predatory practice Jimbo.
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