cm in brand/comms always focuses on big brand/comms stories (getting the biggest customers to do the most high production stories) - I've found it's a lot better suited in PMM - tends to get a much more broad and influential scope around creating evidence for multiple functions, running lifecycle marketing programs, etc
Still always a challenge because customer marketing is a catch-all term that encompasses customer advocacy and content generation, customer reference, can mean lifecycle marketing upsell/x-sell in a SaaS context. depending on what's in scope it's then easier to decide what function it belongs to.
E.g. for Sarah if it's more upsell/x-sell/lead gen from customers then it does make sense in demand gen. but the content/evidence piece definitely has more affinity to PMM. (which neighbors sales enablement)