What does “against local authoritative advice” mean?

Our travel insurance policies cover off piste activity subject to you not being alone or acting contrary to local authoritative advice.  This means that you will not be covered for going off piste if this is against the guidance of anyone you should reasonably have checked with and listened to.  This is not an onerous requirement.  For Insurers to avoid a claim, they would have to show that such guidance was readily available and that you ignored it.