Hey, you've described the old soft-sided Trager briefcases I keep in the corner of my office and at home, each holds a bulk volume of basic medical supplies (kerlix, triangle bandages, 4x4s, ABD pads, gloves, masks, scissors, cheap rain ponchos). The only thing that qualifies them to hold medical supplies is an expandable middle that hold alot, and some outer pockets for some incidentals (splinting materials and a first aid reference mostly). They look something like this, only more beat up.
http://www.bagsbuy.com/trager-540r-everyday-expandable-brief/22324/22324 They're reasonably water resistant and they were free, about 10-15 years ago I bought them to hold laptops, but since retired them. I can sling them over my shoulder and move, alot easier than the plastic box I used to keep bulk supplies in. So I filled them up with stuff I may need after a 9.0 quake, something I can grab and go outside and start tending to people. Enough for probably 30-50 wounds at the moment. It looks nothing like a medic bag, but I'm not a medic. And its not a well-rounded First Aid Kit, I have one of those separate to rely on for medical essentials. I work in the middle of what will likely be a mass casualty area. I bring supplies to where we can expect wounded, and if they're used up I don't really care about getting the bag back. I would probably be alot pickier if I bought one of the fancier $85 medic bags purpose built to zip out and expose the innards.