That's one of the reasons anonymity is important for this solution, but it can be only partial anonymity as trust needs to be put somewhere and the it's likely to be on the platform.
Say, the platform collects the original bills from the patients and publishes redacted data in a single common format. So, if a user asks the platform What will be the cost of X treatment in Y hospital? The platform can return data based on the occupation of the user as that's one of the important factor which private hospitals use for discriminative billing.
With enough data (bills) one can find more insights about the billing practice of the hospitals and even insurance companies as they play an important role in private hospital bills.
I think this platform needs to be a Non-profit NGO in-order to gain trust among users and to face the lawsuits from the private hospitals. But, at the end of the day if the platform solves a real problem; nothing can stop it from functioning.