From a euphemism for being suspended on full pay pending an investigation. You aren't working, and you can't work for a competitor, so there's not much to do but potter about in the garden.
(The term originated when the paid white-collar workforce was still overwhelmingly comprised of men who weren't responsible for housework or child rearing.)
Thank you for your comment. I can't speak for the entire world, but in the UK a 1 cm" gap in the door of a public toilet would be massive and unacceptable. It's not enough that someone can only see into a stall through a gap in the door if they are "right up to it"; they should not be able to see in at all. Public toilets in other countries have doors with gaps you can't leer through at all.
Re. the "gaps meaning ventilation", surely the "big gap at the bottom" and the fact that the whole top is open will be contributing more to ventilation?
You say you think this might be a regional thing in the US. Okay, could be. I have personally encountered this issue in Washington, California, North Carolina, DC, Massachusetts, Georgia, Texas, Oregon, Ohio, Illinois, Indiana, Virginia, Pennsylvania and Maryland.