Insurance contracts usually exclude liability in cases of negligence or breach of the law (try getting a rental car damage paid for by insurance if you'd had a drink..).
I looked at my policy, and voila:
AVN 94 – Breach of air navigation regulations clause
The cover afforded to each Insured by the Policy shall not be invalidated by any act or omission which results in a breach of any air navigation or airworthiness orders or requirements issued by any competent authority
affecting the safe operation of the Aircraft provided that the Insured so protected has not caused, contributed to or knowingly condoned the said act or omission. Any Insured who has caused, contributed to or knowingly
condoned the said act or omission shall not be entitled to indemnity under the Policy.
(My bolding.)
As the pilot in this case seems to have admitted to causing the breach (taking a passenger while conducting emergency practice), he might be in trouble.
If you are employed, it may be a different game altogether as employers usually have some sort of employee liability insurance on top of the asset (read airframe) insurance.
In this case, it depends on the wording of the contract the operator of the school/rental business has with his insurance, but I certainly wouldn't go round and tell stories if I had just pranged an airframe
