So the best solution to this will depend on the exact use, datasource (live or TDE)...etc.
So yes filters do (as you'd expect) filter the data! The 2 ways round this are (in not particular order);
1. Replicate the data-source and use a blend (that way you can filter one, but not the other and blend in the 'Peer Averages'
3. Use FIXED LoD calculations. Due to Tableau's order of operations, these are calculated before the filter is applied, so can show the filtered value and 'peer averages'. The dis-advantage of this is that for large data-sets they can be a little slow (by Slow I'm talking relative to the usual instant-ness, so like 3 seconds rather than 1), and are not supported on some DBs, if you are connecting Live
For completeness there is a 4th of using Table Calc filters, but I don't think this will work here as they can't be applied across multiple sheets off a single drop-down (again due to the order of operations, these are calculated later in the pipe so can filter the view without filtering the underlying data.
Let me know which one sounds best candidate and I can show you how.
Yes a packaged workbook would help. So just need a few rows of data (maybe 100 or so) with doctors (anonymize the names), patients (again anonymize the names), and some other metric (say patient age group/***).