I suppose this is an oversight and should instead be "below or equal" setting rather than strict "below".
Examples for comparison:
Input limiter set to closest non-zero value (20 for tier I storage). Storage is connected to both input and output belts and works as a buffer.
Expected behavior - storage pulls items from input belt if its current content is less than 20. As soon as the storage has any items it immediately outputs it to output belt - items are passing through.
Actual behavior - same as expected, works as intended.Input limiter set to zero value. Storage is connected to both input and output belts and works as a buffer.
Expected behavior - storage pulls single item from input belt and immediately outputs it to output belt, maintaining zero content at all times. If storage can't push items to output then it's not pulling any items from input belt, also maintaining zero content.
Actual behavior - storage not pulling any items regardless of output capability. This is equivalent to just pausing the input belt.
Also same issue with output limiter. There was a report about a month ago where Cpt Marek explained that this is intended behavior. I still don't get why it works in such way.