Absolutely, keep that bit of burnt cable to show them to prove your point, FFS! I don't want to alarm you but that burnt cable had the potential to start a fire. Good luck and I hope all is good now!
If any over current protection device is tripping it is because there is a fault, it is what they are designed to do, I personally would have disconnected that particular circuit and investigated why it was tripping, if there is sign of any damage to a cable leave the power off until it is...