If an outside agency calls and offers assistance the person dealing with the event sees only problems with accepting the help. There will be more coordination needed, what about reimbursement for their services—all these issues come to mind and, “After all, this will soon be over.”
But then, it isn’t over! You are 72 hours into the response, dead tired and all the institutional knowledge of the event is in your head. How could you possibly incorporate someone else into the response since it will take too long for them to come up to speed. And, after all, "It will soon be over."
I say that we need to learn to accept help and practice receiving help from other people and agencies. By doing so you will be better equipped and confident in grabbing the rope and knowing that help is on the other end.