Is it possible to have an image be picture-in-picture and just tell FCPX to keep it at its original size?
By "actual size" I suppose you want to conform your footage pixel to pixel instead of frame to frame. For this you will need to change Spatial Conform to None in the inspector.

The new default behavior in FCP is to scale your footage to either "fit" or "fill" the project's frame, the difference being only relevant when your footage doesn't have the same aspect as the project's. This conforming defines the actual 100% Scale in the Transform panel. So make sure the scale is also set to 100%.

You can find more information about Spatial Conform in it's documentation.