Early last year, executives at a small hospital an hour north of Spokane, Wash., started using a company called EmCare to staff and run their emergency room. The hospital had been struggling to find doctors to work in its E.R., and turning to EmCare was something hundreds of other hospitals across the country had done.

That’s when the trouble began.

Before EmCare, about 6 percent of patient visits in the hospital’s emergency room were billed for the most complex, expensive level of care. After EmCare arrived, nearly 28 percent got the highest-level billing code.