There are no absolutes of course but I tend to think when a cat is going on a bed or a wall near a window or on their human's clothing or something like that then it's more likely that it is some sort of territorial insecurity (I.e. Stress). But if your kitty is marching right over to the box and going right outside the box, then I think it's more likely that she is telling you that there is a problem with the box. That it's "owned" by another cat, or that it is too small, or too smelly, or has the wrong litter, or perhaps it's a hooded type and she wants open. Another possibility is that she knows where she's supposed to go, but that it's hurting her to go and now associating that box with her discomfort, so she's trying something else to alleviate the discomfort. So if you notice her straining to go, or there is blood or mucus or runny poo, then would be a clue that it is some kind of discomfort.
One other comment... I'm not really sure that a closet is going to be an acceptable place for a box for many cats. To solve this it may require you to experiment with other box locations. My suggestion would be to start with a really large non-hooded box (in addition to what you have now) and leave it out in the open somewhere, then observe the usage patterns and learn from it.
Then when/if she goes outside the box, really take stock of the state of things. Is there poo or pee in the box when she rejected it? Where was the other cat at the time? What does her poo look like? Etc.
_________________ The little monsters 3
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