Insurance denies claim for new patient charge for new pediatrician after we moved

My family and I moved to a new neighborhood back in April. We have a two year old who had been seeing the same pediatrician since she was born, but now that we’re moved, we found someone else. Of course, this new pediatrician is not in the same physician group or anything, so I believe they did a new patient evaluation on my child — which makes sense to do. However, this charge was denied by insurance and in the denied claim, it says:

INIT PM E/M, NEW PAT 1-4 YRS

You are responsible for this charge. We have paid the maximum amount covered by your plan for this service.

I did my best to research the procedure code and situation, and my interpretation of what’s going on is that insurance will only pay for the evaluation of a new patient every 3 years or so? Since insurance already paid for this evaluation with the first pediatrician visit after she was born, they are denying another evaluation charge with a different pediatrician, as it’s only been 2 years. This was otherwise a normal, scheduled pediatrician visit to get vaccine shots (these claims were covered).

I just want a gut check to see if this is normal? I don’t mind paying this charge, but only want to do so if it is actually my bill to pay.

Thank you.