Once you sign and let him tow the car, you risk to pay massive repair fee ( maybe no repair at all ) and also risk they remove your car original parts for some cheap parts.

Never sign anything. Call your insurance provider, or your authorised service center. Better to tow the car back to your workshop. If you really need the tow car service for some reason, never sign anything, pay them to tow the car back to your workshop (with you in the tow car).

Sometimes the police will work together with the tow truck, urging you to tow away the car immediately or he will give you a saman. People will then sign due to fear and panic. Just tell to police if wan saman, then go ahead, or ask the DBKL to tow it away. Never sign anything as your signature means consent for them to do whatever they want.

Most tow truck works to cheat your money and perhaps remove your original parts of your car.
Their aim is to make you sign and your case is lost once you signed.

Do you think so much of the car behinds you and prepared to get scammed? Of course if there is option, I would push my car to the side. But definitely no way to let them tow the car.

Things will be difficult if the driver decided to tow your car to his workshop instead of tow your car to safe location. Then you have to deal with thugs on your own. Do you want that?

I rather get a saman or DBKL to tow the car back to their compound. This way you ensure the safety of your car and maybe fines few hundreds rather than few thousands (and maybe not even a good repair) from the scammers.