Always worth checking the insurance, with a full disclosure of the situation.
There are two cases to consider, both legal
1) the plane is insured with a particular pilot flying it
2) as above, with the pilot being himself insured
The two are very different things.
If you own a plane, or are in a group, then your name should be on the policy, and you are in 2). So if you prang it and there is a 3rd party (or passenger) claim, they insurer can't go after you to recover what he paid out.
A normal renter, or flying student, will be under 1). You are not insured.
Another thing is this: my insurance covers me (named) and also covers me for receiving any training. It stipulates 500hrs and a PPL/IR as a minimum. Now, what if the instructor has only 200hrs? Many PPL instructors have only that; my first PPL instructor had 150hrs. Under FAA rules, the student is usually PIC so it would be OK. But in a G-reg, the instructor is AIUI always PIC (even if the student is legally capable of being PIC)...