Sorry, machine doubling. It is flat and shelf-like. And for future reference, doubled die. Keep up the hunt!
Yes, a it is possible for a coin to be struck with doubled dies on both the obverse and reverse. That possibility is extremely remote but it has happened and there are only a very few such examples. (Sorry but I cannot recall an example at the moment.)
It is uncommon, but not terribly so. For instance, you've got the 2004P 1DO/1DR-001. There are a few other doubled columns/DDO combos. And there are a few examples in the 1940s of class VI DDO/DDR combos as well, so I wouldn't quite call the possibility remote.