Indeed.
Only one person can be PiC at any given moment, and they can log it. Signing the tech log is one common indicator, but the crew logbooks are the normal source of this information.
For many years there was no legal requirement for insurance in private aircraft anyhow in the UK, and I'm sure there still is in some other countries. So insurance is a red herring.
And even an illegal flight is still a flight and has a PiC; else who is there for the CAA to prosecute for it?
G