There is no liability without proof of negligence (which means failure to maintain a reasonable standard of performance in the activity concerned, be it flying, driving, or whatever). Negligence is sometimes presumed. For example, in a case where pilot and passengers die after an aircraft stalls and spins in from the circuit, with no evidence in the wreckage of mechanical fault, airframe failure, overloading etc, it might be said that the accident must have been a consequence of careless loss of control through incorrect control inputs. Otherwise, the borderline between error of judgment and negligence is particularly difficult to establish in activities which involve large elements of judgment and of risk, such as aviation and mountain sports.
Most insurance claims are settled without involving lawyers. If a claim is made which has no merit, the insurer should fight it on your behalf, although it might make a nuisance value or commercial settlement depending on the apparent strength of the claim and the likely cost of resisting it. Insurance can protect you not only against claims for which you are liable, but also against hassle and expense where you are not to blame.