As you said... two unrelated items. And not even caused by the property itself.
And I'm a bit baffled why you would be in any way offended about missing sleep when it was you that called the FD? Or would you have preferred they called you again in the morning to inform you about your package? Noisy neighbors is outside of the control of any property, and they seem to have handled it perfectly fine by offering an apology and sending security.
Don't be cheap, pay the $6. Handling these things does cost money. Or at least wait with complaining until it actually shows up on your bill. It has been a rather regular occurrence for me that the charges were never actually charged (no idea if this was because of status).