Disconnected battery while engine running

I think you will be fine, though I would never perform a disconnect while the car was running. It's an old school way of testing that the alternator without using a multimeter, if the car continues to run with the cables disconnected, you know the alternator is still charging the car, but it is not without risk of damaging the electronics in today's newer vehicles. If the vehicle is running fine with no fault codes, and everything works, then no worries at this point.

As long as everything is working as it should then the vehicles electronics didn’t suffer any damage. The tow company dodged a bullet, but I would call the tow company and get a hold of someone in management and let them know what he said to you, he is setting them up for a loss. You never ever disconnect a battery cable with the engine running on any vehicle with computers. I had a customer that did this to his car and back then it cost him every electronic component the car had, it even took out the radio. So yes believe that doing that is bad. While we are on the subject of batteries in computer controlled vehicles, you also should never disconnect a battery without using a memory saver tool, it plugs into the OBD 2 port and powers up the KAM circuit so the computers can keep the basic programming active. Drive with care out there.

The tow truck driver is an idiot .