Having experimented with it a bit, I've realised that it's not counted as part of the inventory space - you can store a 'unique' item in there and then add a second one to your inventory. (So, another place to stash phoenix downs - and also useful if you want to put some quest reward costume pieces into your glamour dresser but don't want to lose the actual item, as I did for a certain sentimental one. Put the original in the saddlebag, bought and converted a replica.)
Anyway if it's separate enough that the game can't tell you're doubling up on unique items, then I'm not surprised if it's impossible to make it display on the inventory menu tab, as nice and sensible as it would seem.