Display Results As / Related Contacts Search exports original contacts instead of related contacts

If you do an advanced search using the Display Results As / Related Contacts search at the top of the page, trying to export the related contacts exports the original contacts instead. I've experienced this on a client site on 4.4.5 in Drupal, on my test site on 4.5.4 in Drupal, and on the demo site in 4.5.5 in WordPress.
Here's what I did on the demo site.
1. Go to advanced search. Search on all contacts. Yields 206 results.
2. Edit the search criteria and change the Display Results As field to Related Contacts, then choose Parent of.
3. Hit search. Yeilds 40 results. Select all 40 contacts and select Export Contacts from the drop down.
4. Whether you export the primary fields, or choose the fields to export, you get all 206 original contacts instead of the 40.
5. This DOES NOT happen if you follow the same process but use the Relationship selectors down below instead of the Display Results as / Related Contacts fields.