It's messed up that the transparency on how it all works is non-existent, and there was no way for you to know what your out of pocket cost would be when you signed the form they gave you during the visit.

I would recommend that next time you have a well child visit you request at the start of the visit that you would rather have a separate appointment for any services provided that won't be covered by the well child visit. The convenience of not having to come in for a separate appointment can be overshadowed by the frustration with getting a bill after an appointment that included preventative care.

Remember that charges submitted are not necessarily based on time. So your statement that you were with the doctor for less than 10 minutes makes the situation more aggravating for you, but has absolutely no bearing at all on what charges are supported by the services provided in this case.

You were provided preventative services in the form of a well-child visit. Your insurance covered the charges for those services.

You consented to receiving non-preventative services when you signed the form she gave you during the visit.

A referral to a specialist (even for a known issue) is not a preventative service but it is a treatment, so you were also billed based on the doctor performing non preventative care medical decision making (the decision was to refer to a specialist). It's unfortunate that this whole situation was not made clear to you before or during your physical visit. It's great that your insurance paid $376.07 of the visit, and you weren't on the hook for the entire $476.07, but even that rate was set by your insurance and not the clinic where your doctor works.

I imagine that you are frustrated that you got billed for the medical decision making to refer to a specialist, because it was so simple, obvious, or otherwise a no-brainer. If that is the case, I would remind you that you had a chance to decline the non-preventative care when they told you that you needed to sign the form agreeing to discuss non-preventative care. Additionally, as the stories go the factory mechanic charges $1 for the bolt, and $999 for knowing where to put it.