**Confirmed.**  
The path seems to use a default sort key on `last_activity_date` and that corrupts the filter somehow. (I checked for caching by waiting more than 1 minute and by varying the question ids.)

If I create [a new filter and explicitly specify a sort key on votes][1], it [worked for a time or two][2] (no `last_activity_date` returned).

But somehow it still inserts `last_activity_date` randomly on subsequent runs. I haven't figured out the pattern to it yet.

As a workaround for this bug, always specify a sort key that doesn't rely on a field not returned by the filter.


  [1]: http://api.stackexchange.com/docs/questions-by-ids#order=desc&sort=votes&ids=857455%3B857454&filter=!8IgsXbMxnbGlR3L4_diGD&site=math&run=true
  [2]: http://api.stackexchange.com/2.2/questions/857455%3B857454?order=desc&sort=votes&site=math&filter=!8IgsXbMxnbGlR3L4_diGD