It is possible to load sensitive data into Auto Insights (my organisation does it). I believe we do use an onprem solution in our local cloud. I'm not the expert on that side of it though - but don't give up hope! There's always a way.
Yes, we'd be more than happy to discuss in more detail what you're looking to use Auto Insights for and the options available to you. As @Nick_Thomas and @IraWatt have mentioned, many customers use Auto Insights with sensitive data.
Is there any specific information you would like?