Setting background-color: inherit does cause it to take the background colour of the parent element.
The reason it is taking transparent is because the background colour of the parent (the li) is transparent (the default value).
The only other element in your second JSFiddle which has a background colour set is #unknown_background, which is the anchor’s great-great-grandparent.
Add div, ul, li { background-color: inherit; } to the end of your stylesheet and the background will be inherited all the way down and the border will not show up.