If it's a motherboard failure, then the issue is unrelated to your Apple account and I don't see a reason why the technician would need your Apple ID password. I can't find any official Apple source saying this is necessary, even for official Apple technicians. In the future, it would be a good idea to do a backup of the device and then reset the device to factory default settings before sending it in for repair. More info is available here: https://support.apple.com/en-us/116942