There is a persistent myth in strata that the scheme is not liable for events not covered by strata insurance. Owners have to look at this another way; they have chosen a policy, probably cheaper, with defined coverage. Which mean that they are only covered for their statutory liabilities and up to the amount the policy allows. If the claims are greater than the agreed benefits, and the injured party successfully sues for damages, then the scheme has to find that money from its existing funds or additional levies.
This is a case you might take to a medical claims specialist lawyer or, preferably, reach an amicable agreement with the owners corporation and save both sides legal costs. So yes, you would have to initiate a separate action against the scheme if you thought you had been unreasonably inadequately compensated.