As a simple point of note, at my unit, if the aircraft in question is airborne then ATC can upgrade/downgrade the incident as deemed appropriate.
If the aircraft is on the ground it is the Airport Fire Service’s responsibility to upgrade/downgrade the incident.
There are many factors involved in the response to each emergency by outside services (including, perhaps for hospitals, moving existing patients, clearing non-urgent operations, etc.). It seems eminently sensible to downgrade an incident once ‘facts’ are established. On the other hand, you could play it out.
Those are decisions we make. That is part of our job.