Jewel,
I think it may be a matter of technique. And maybe not. Try this: On a Word Processing document, one with a text layer but without any graphics, mouse around on the page and notice the shape of the cursor. It should remain a vertical bar with little curly arms and legs - the text insertion cursor. Now let the cursor wander into the menu area at the top and it changes to a selection arrow.
Mouse back into the text area and stop in a margin. Now press the Command key. The cursor should change to a selection arrow for as long as the Command key is pressed. With the Command key still pressed, click-drag the arrow. A selection box will be created - a gray rectangle that stretches as you drag.
Any graphic object intersected by the Selection Box should become selected, whether it's declared a background object or not.
Place a couple of shapes over the text. In the Wrap Inspector make each of them Floating and Deselect the Object Causes Wrap Option. Now, Arrange > Send Object to Background on one of them.
Look in the Wrap Inspector and assure that Background Objects are Selectable is un-checked.
Mouse slowly over the two objects and note that the cursor changes to a selection arrow over the top graphic and not when over the Background one. That's because you wouldn't want the Background object to be selected when you are trying to select the text that's over it. So Background objects have two characteristics; a simple click will not select them when they are under the text frame and by default they will repeat on every page of the Section.
Click on the top object to select it, and off of it to deselect it. Note that the selection handles appear when selected and that they are filled with White. Confirm that clicking on the Background object does not select it.
Now go to the margin, hold the Command key until the cursor changes to an arrow and Click-Drag a Selection Box to intersect the Background object. If this doesn't select the Background object, you have a rare condition, one I haven't seen, and margin changing would be in order.
By the way, once you have selected the Background object, note the that sizing handles have Blue fill, identifying them as Background.
If you conduct this exercise, let me know how it works out.
Jerry