The ajax request fails because the object in question has been deleted.
If you try it with an object that still exists (e.g. http://www.openstreetmap.org/api/0.6/way/666/full), your jQuery code should perfectly work. Or if you grab the full history of the deleted object (http://www.openstreetmap.org/api/0.6/way/252570871/history), but that's probably not really what you want, I suppose.
It should be said, that the API probably should also send the CORS-headers for the failing (HTTP 410 Gone) requests, so that your client can detect the error code. This looks like a bug that should be reported on github.