That's a great narrative for a lawsuit, but I'm skeptical it's true. It's possible they were negligent (it happens to straight people too wouldn't you know it!), but it's also equally possible they were making every effort and they're still getting sued because our system has enormous financial rewards available to those who win successful lawsuits, even if they are disproportionate in many cases.
At any rate, no, there is not some systemic bias against any class of people in our medical system. ERs take care of anyone, medical insurance or not. Our medical professionals are highly trained, EMTs, paramedics, firefighters, nurses and doctors are by and large good at what they do. The existence of exceptions does not discount the rule.