@Christopher375
As per Airbnb's own T&Cs, this absolutely does not qualify under the Extenuating Circumstances policy.
Only the death of an immediate family member is covered by EC, while serious illness only applies to the host, guest or any member of the travelling party, and not to immediate family members. So it doesn't matter whether the injured party is a close friend, a twin or a distant cousin, twice removed - EC is not applicable here.
Quote the clauses above back at Airbnb CX - over and over again, if necessary - until they agree to abide by the terms of their own policies. Don't let them bully you, or allow them to deceptively deprive you of income that's rightfully, and legally, yours.