Great topic. I agree with Daniel's comments and have struggled a little bit with this in providing good customer service especially where an escalation is involved, however, we've been able to successfully modify our processes and practices within Holacracy.
Just curious, how long has Company X been practicing Holacracy? Did your customer experience with an issue or escalation change between before and after Holacracy? If so, would it be correct to assume that the typical path for a customer escalation would quickly get into a manager's hands who would own and resolve it? If there's now a gap in a process such as a customer escalation, then I should think it would need to get resolved in Governance via a Role, Accountability, or Policy, et cetera.
Also, I agree with your comments as a Customer, that you want to connect with the soul and the rest of company should be somewhat transparent, i.e., how they're organized or resolve your tensions or issues should remain backstage, so to speak, and you just experience the magic upfront.