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, it worked for a time or two (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.