If you make money off them but save them more money than you costs, it is still towards their benefit. The only problem occurs when you start working with the hospital to create even more arcane bills that you get into immoral territory.
That's exactly the circumstance I outlined previously. This plan has you taking the debts of somebody who cannot afford to pay, reducing them to something above the actual cost, then asking them to pay the higher amount. You are making money from the least able to pay and profiting from a system driving people into bankruptcy. I cannot imagine starting such a company without serious empathy issues.
I'd start with a mentally forced mashup for each to get a few that might work. e.g. "If i've got to make money by lead generation with a medical bill review service/app, how could i do it?"
Then i'd focus on how we'd drive value to the consumers.
Then think about driving value to others parties who may be willing to pay for something similar.
ie would pharmaceutical and medical device companies be willing to communicate directly with these consumers?
note i'm not saying its easy by any means, but i do think its a real problem that could take off if an elegant and worthwhile solution came about.