Would the EMS service allow a second unit to RESPOND to a lift assist?
They better. If not, I'm sure the fire department will come if you call. Heck, they'll come and rip walls out if that's what you need to move the patient. Like it or not, we're in a transport business, and getting the patient safely from Point A to Point B is a key part of what we do.
If we look at the story in a different way... say.. how about the pt died on their stretcher while waiting for a lift assist to arrive. Wonder how the conversation would be then?
Well, first of all, were that to happen, the patient would die in bed, because they should be waiting for the lift assist to even move him to the stretcher. And in that case, the blame would fall on the service that didn't send the right people and equipment.
Or it would simply be regrettable, but nothing anyone can help. In my area, two of the local services operate bariatric units. Neither generally operates 24-7, and if you need a bariatric unit at night they have to pull multiple rigs off the road to get two bariatric-trained EMTs. It can take an hour to get the specialized ambulance on scene. If the patient is having a heart attack, you either improvise, adapt, overcome.... or the patient doesn't get to the hospital and is DRT.
The bottom line here is either move the patient safely, or get more help. You should know how much you can handle. We all know that even a 250 lbs patient is heavy when its dead weight, and this patient was way more than that. The last thing we want to do is make the patient worse by dropping them.