Wow...I seriously hope you're kidding. We have fire respond to all of our calls, but even at 5' tall and 125 lbs, I still lump all of our bags, equipment, cot and yes stair chair. (Our stair chair has a weight limit of 350lbs) If the patient is a little heavier than what I'm capable of handling, then yes, I do ask for help.
It's not their job to do our heavy work, rather assist us when needed. I worked for years in a rural setting where we had only volunteer fire guys and they weren't available during they day, so we did it all.
Unfortunately, it's attitudes like that that create hostility between the two services.