Client does not see CSM as source of truth, default is to try and connect to other team members

I lead a success team at a software company. We have an instance where a client constantly asks to be connected with other resources in the company beyond the CSM. It sometimes is a result of the CSM setting epectations or delivering news that is out of scope for our software, but most often it is just he default for the client to ask to be connected with memebers of the product team or leadership. Our company does not operate that way, we run lean and there are not other resources to speak to on principle of prrotecting people's time.  I would love some talk tracks or strategies to get this person to understand that her point of contact in the company is the CSM, and what the CSM says goes. How have you in the past built up the CSM as the source of truth for a client whose default is "escalate"?