Hi guys

I was hoping to get some advice for my situation. I recently got into an accident with a taxi, and all things considered, I admit I'm at fault.
The thing is, even though I already told the driver and the operator that the vehicle would be fixed under my comprehensive insurance, they didn't want to accept this because of the "abala" of going through the insurance process, when they could just have it fixed at their neighborhood talyer for much quicker. Note the damage to the taxi wasn't THAT bad, it doesn't prevent the taxi driver from being used.

We were discussing for about an hour, but eventually I got tired because I needed to be somewhere else so I just gave them 2500 to have it fixed themselves, after some haggling.

My question: I'm fairly certain the proper thing to do would have been to have it filed under insurance, otherwise what's the point of getting CTPL if no one's going to use it anyway due to perceived inconvenience, right? But how to deal with this situation?

Thoughts would be greatly appreciated. Thank you!