canbera, the same is pretty much true in the civil world. The theory is that the local authority services take over and permit the Airport RFFS to replenish media etc and provide cover again for the airport. Whilst the minimum levels of media and personnel readiness set out in the licence are not available there should be no operations that require fire cover.
In practice, if there is an accident in which people need to be rescued from the wrteckage, it will usually be too late by the time the local authority services get there. If this is not the case, I can't imagine a situation where the two services wouldn't work together (not sure who would be in charge though).