Some of the storage items (tents, barrels, backpacks, etc..) have their inventory collapsed by default. Try hovering over the tent in proximity view and clicking the right trigger; this should expand its inventory for use.

This may not pertain to what you are saying, but I have noticed sometimes the inventory for backpacks/barrels is collapsed by default. You could try hovering over the backpack in your inventory and pressing R3/Right trigger to expand its inventory while its equipped.

I can also vouche for this issue, Ive had the same exact thing happen on 2 separate occasions post-1.10.