Quite right. If there is a fire in your house, it is still an emergency even if you have an extinguisher and evacuation plan.
Why do I feel like this thread is giving the word emergency an existential crisis :)
To be an emergency or not to be an emergency, that is the question!
An common use of "emergency" in a similar manner, if I have stomach issues and need to use the toilet now, I will call the situation an emergency even if I haven't yet soiled my pants. If I reach the bathroom in time, the emergency ends with no major incident.