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First, you need to send written (do not use the phone) notification to all three credit bureaus that the debt is a medical bill in dispute with the provider. The credit bureaus addresses are here. Copy the medical provider with all of the letters as a cc.
Second, after sending the letters above. Send a letter to the medical provider - at their service address and to their agent of service (look up the agent of service at the Michigan Secretary of State online service) do not send to the doctor's office. They will claim it got lost. In the letter state clearly the agreement and that you are willing to pay $250. That you will not pay the remainder and that it is a disputed medical charge and why it is disputed.
In most cases they will accept the $250. Sending to collection would result in a recovery of the $416 less a 30% charge or less than what you are offering.
If it is sent to collection, you already have given written notice to the credit agencies what is going on. The first collector that calls (not the provider, a third-party collector) demand an address. Send a letter to them immediately asking for them to "prove up the debt" and telling them that you will not pay and they will need to pursue court action.
Now, I will tell you in most cases, you have signed something agreeing to all charges and if the med provider "wins" in court, the costs of collection will be added to the bill and you will have the collection noted on the credit rating.