My oregano isn't prostrate and it is just the regular old, unnamed Origanum vulgare variety. The plants are not the strongest and use the rest of the patch for strength when they have grown long and lanky - which they do if you don't keep them clipped. If they don't have enough support, they will flop over and then need to crawl and sprawl. Try keeping your plant clipped more regularly to encourage a more bushy habit.

FataMorgana