The expression "skeletons in the closet" has always seemed rather grim. But it turns out, it's more literal than it is grim. Now a days, most people are very familiar with the expression "coming out of the closet" or being "in the closet". To understand another layer to the expression, you need to realise that the skeleton that is in the closet is not that of a dead person. These individuals are in-the-closet about their skeletons. Their bone structure. They aren't out in the open about their skeletons. So their (own) skeletons are in the closet.
A monologue about bone structure from the movie Paper Moon.
Related page on pregvestigation.