why is my Database Engine Tuning Advisor trying to create statistics, even when I'm using "auto create/update statistics"
Auto Create Statistics will not create multi-column statistics, only single-column. Indexes will create multi-column based on the index automatically, though. 

So DTA is simply recommending statistics that don't exist as indexes already. 

Most people don't recommend DTA anymore. I don't think it has been maintained for a few years now.  Lots of other tools like sp_blitz will recommend indexes a lot more intelligently.