The distinction matters both because the precise wording of specific contracts will cause distinctions that were not adequately considered by certain participants, and also because of who enforces the contract at a human level. Who determines what does and does not qualify as a natural disaster? If that entity has a stake in one outcome, or is influenced by an entity with a stake in one outcome, that changes the outcome. Both of these are seen in insurance claims, where homeowners find out that rising rainwater does not actually count as a "flood", and where agents of the insurance company are financially incentivized not to pay out at all if they can help it. These factors do not go away just because you take away the insurance company, you've simply diffused them.