Rose pogonia orchid?

While hiking out to the cliffs of Georgian Bay at the end of May, we passed this little wildflower growing in lowland boggy areas along the trail. I wondered if it might be an orchid and it turns out that it is! Rose pogonia (Pogonia ophioglossoides) is a native orchid also known as snakemouth.

However, I have just done a little bit more research and now I wonder if this is not an orchid but a member of the milkwort family called Fringed Polygala. It was growing very low to the ground and I think that Rose pogonia is taller (6-8 inches). Also, the flower we saw had only three petals. Alas, I think I was foiled, but now I will have to watch for Rose pogonia orchid on future outings!