Let's put it this way, your chances of the fire station being empty is by far greater than you will wait longer than 20 seconds to talk to a 911 dispatcher.   

And FWIW your are correct that the response time clock for first responders begins ticking when the call is answered.

911 call handling and dispatch is tracked differently.

I think NAFPA says medical and fire calls are to be dispatched within 60 seconds of picking up the phone 90 percent of the time.  This is a lot quicker than having just a 60 second average. 

Then a tougher time standard kicks in,, first responders are supposed to be enroute within 6o seconds of the alarm activating.  Fire misses this standard a bit,, AMR which tends to have crews standing-by in their rigs, is in compliance.

AMR gets fined not being in compliance,,,nothing happens to Fire.
I'm not sure at this moment 

BOEC also has goals for emergency police call handling, but I will abstain from any further remarks about these til I confirm those goals.