Question about outswing door on attached toolshed
Sometimes sheds just are not built like standard construction.  You are right that the door is mostly hung on what appears to be brick molding.  If you want real strength from the hinges and the latch side of the door, setting it back into the opening where you can grab studs is going to be your best bet.  Having the door inset a bit also makes prying attacks a little harder (not much, but something) but the main goal is to get all of the hinge screws and latch plate screws into a structural member.

On the plus side, it looks like the stop molding is just nailed onto the door casing rather than being a single piece of casing with an integrated stop, so moving the door back into the opening might be a little easier.