>I developed and published both of Power BI Pro (Cloud) and enterprise (on-premise). There wasn't any restrict about on-premise edition and it has auto-refresh feature. What made you think on-premise edition hasn't auto refresh feature? Actually on-premise edition doesn't have auto-refresh feature because it has data every time and when you want to run report it get data from server. We had SQL server batchs to send report data to Power BI on-premise edition datawarehouse periodically. Or you can decide to don't use a datawarehouse and your Power BI reports get live-data when yo run report. You have all options with on-premise (Enterprise edition) edition.
The wording on MS' website is very confusing. Bottom line (as you said), someone can deploy a PBI report to PBI On-Prem report server, and set up a schedule in the PBI Report server to refresh the data on a schedule. That data can come from an on-prem data warehouse, or even a database up in Azure.
MS has, in my opinion, not done a very good job in communicating what PBI On-Prem Server can do (and what it can't do). Their policy of 3 releases a year pretty much resonates with their plan that they want everyone pushing PBI content up to the cloud.