Nope, you are correct!! You can put the private/separate box in a shed, or even a garage. Don't put the box outside. Just remember to keep the private box pretty dim (since hens tend to like darker locations to lay eggs or even when they want to brood, so don't put a light in her box)
PLEASE READ VERY IMPORTANT: I'm not sure if you know this yet, BUT since you are going to create her a private box your going to want to move her from the old location to the new private location.
And so how are you going to do that?? Well the best way that chicken owners have done it, is to move her at night not in the day because this is when she cannot really see anything and is more unbothered at night. So your going to start of with sneaking all of her eggs from her first (try not to use a flashlight while your removing the eggs from her). Then properly put her eggs into the new private box. Return back, and carry her up from her old location to her new private location
AND PLACE HER DIRECTLY ON TOP OF THE EGGS. After you have done that, leave her alone and check back on her on the next day and see if she accepts the new location. Most of the time the hens will accept the new private location and sit back on the eggs.
However, in some cases hens will abandon their eggs and try to move back to the previous/old location. (pretty rare though)
Before you do any of this, make sure to set up everything she needs in her private box (water bowl of her own, feeder of her own, her nest box, and bedding etc..)