When Firefighters call a "Mayday", in this case multiple firefighter's trapped / injured etc, and it gets broadcast over a main channel, it's a "Ya'll Come" call. Multiple Fire / EMS back ups get called in LE show up in hopes of being able to help etc. Personal opinion, is there is nothing more there than that. Retired Firefighter Anon.
Clusterfuck's are what we are used to. When shit goes south, embrace the suck and deal with it.
On an incident where "an explosion has occurred and FF's trapped", dependent upon the locality and protocols, mutlitple mutual aid units would be dispatched, including LE, worst case would be toss an injured FF in a cruiser and run. To rescue one firefighter from say a floor collapse into a basement, could take up to ten rescuers to pull that one FF out, now multiply that by 9 or 10.
As for other emergencies where I'm at, other localities in the county "Move up" into Fire / EMS stations for coverage. We have county sheriff's and local PD's can do the same - cover other districts.