Muyleart explained: "So on that call, that's a diabetic that we just ran to help, who was in a diabetic coma when we got there. And he thought he had some money, and apparently he thought we stole his money, so he called 911 back. ... That's what you call 911 abuse."
At times, some of the firefighters can't help feeling that some residents -- particularly those who dial 911 again and again -- are somehow gaming the system.
The routine of medical calls can be grueling, they say. If it was up to many of these men, they'd fight fires all day, every day.
"Definitely fires," Muyleart said.
Consider the numbers: It costs taxpayers about $3,500 every time Engine 10 leaves the station. That's about $3,500, 25 times a day, just for this one company.
But according to Washington D.C. Fire and Emergency Medical Services Chief Dennis Rubin, the system is necessary and effective.
"It does drain the system, it does cost taxpayer money," said Rubin. But, he said, "I can't say no to [residents]."
"I think in any community that has a poor area, less advantaged than others, the service of the fire department, whether it's medical or fire responses, always seems to be on an uptick," Rubin continued. "Also we have a large homeless population in this area and on top of that we have an aging population."
The chief said most firefighters embrace their work, whatever it brings.
"I think they're here to help people," Rubin said. "And I really believe that in my mind, in my heart, in my spirit. I think they put on the badge and I think they've sworn to protect the people no matter what it is."
Making the rounds with Engine Company 10, it becomes clear that there is a huge gap in meeting the medical needs of this community -- and perhaps the community has found a way to fill that gap themselves.
"When you look at the poor people, no one else is taking on those responsibilities," said Rubin. "No one else is doing it."
The firefighters can see it from the residents' side, too.
"I think I guess my personal feeling on it is that maybe it's sort of something that's been ingrained in the culture of the neighborhood here," said Ruiz. "You're sick, you call 911. It doesn't matter what it is, you always have an ambulance that will come, the fire department will always respond and they'll take you to the hospital."
It does wear on the men. There are moments of real frustration.
On one call the firefighters encountered a drunk man in the street with multiple wristbands from hospital stays. He was moaning loudly and moving erratically.
They took his blood pressure. Then they put the patient on a stretcher and took him to the hospital, where for at least one more night he'd be warm, safe and fed.
Back at the firehouse, we asked whether the patient had really been having any kind of medical emergency at all.
"Well, he had a tag on from today and yesterday," said Richard Sheltra, another firefighter. "So he went every day to get something to eat and to stay for the night. And he'll be released in the morning and will do the same routine tomorrow.
Muyleart explained that like so many of their patients, "I've seen him before. He hangs out in that exact same spot."
The hospital has to take the patient, Muyleart said.
"Oh yeah, they have to. Just like we have to transport them."