SharePoint List Filter web parts not displaying on a SharePoint 2010 Page in Edit mode

Our Business Analyst and I recently ran into an interesting problem in which we were attempting to install a couple of SharePoint List Filter and Apply Filters Button web parts on a page that would help users filter items in a connected list.

After adding the required web parts, our BA noticed that these controls were not appearing on the page as he would have expected despite the fact that the page was undoubtedly in Edit mode.  As a result, he wasn't able to configure the newly added filter web parts as well as set their connections to the associated list web part.

Anyway, I just happened to place the list view web part that these parts were supposed to connect to in Edit Web Part mode and, voilà, all of the filtered web parts suddenly appeared on the page.

At that point, our BA was able to proceed with his configuration and connection work without issue.

Thought it would be nice to share just in case anyone out there happens to encounter the same situation.