There is a difference between the airport being 'closed' and commercial airlines being unable to land or depart due to lack of fire cover.
...err no there isn't. If the fire crew are engaged in a response callout and the residual equipment/staff is below required fire cat for the airport; or at the discretion of the airport management any ensuing emergency situation in progress otherwise impedes on the capacity of the airport to operate safely, then the word is closed, period. Any other interpretation of closed would probably be DISUSED or ABANDONED.