I think what's happened is someone's set a background shortcut rule and then looked at the ‘computed style’ resulting from that shortcut rule in the DOM inspector. They've noticed that setting the style also sets Mozilla's background-clip, -origin and -inline-policy properties, and tried to reproduce these rules without understanding what they're for (namely a detail of Mozilla's CSS implementation, and potentially CSS3 in future).
Certainly changing -moz-background-inline-policy would only have any effect on elements that were display: inline (which div isn't by default), and changing the clip/origin properties around the border would only make any difference if the element actually had a border.
Get rid of them.