Correct, we would host the data. I envisioned the client with their own Power BI login that was specific to their dataset/visualizations.
Azure, Amazon and a host of others allow you to set up virtual machines. Where each one of these machines may have its own power BI desktop. I wasn't sure if that would be a good solution for how BI operates today or not. It may be cost prohibitive. I'm still trying to feel out the right solution. Or if Power BI is even the right tool.