In order to understand why this is, think about how companies often do things like giving discounts to people who buy in bulk. The same reasoning applies here.
Companies do want to charge high prices if they can. But they also want to sell a lot of products. In the case of health care providers, they want to sell a lot of health care procedures. If a provider signs up with a managed care plan, they do have to lower their prices. On the other hand, though, they have a huge and guaranteed stream of patients. They know that they will be able to sell a lot of procedures, drugs, and other things that go along with the provision of health care. This is a trade off, but it is generally a good one for the providers.
So, health care providers are willing to accept the lower prices because they want to be able to guarantee themselves a stream of patients.