When you are inside a tent, if you hit tab, you have about a 50/50 chance of seeing the tent inventory. I don't mean "all the items in the tent inventory," I mean that the inventory slots for the tent itself, as well as the tent header for inventory slots, only appears if you are in just the right spots looking at just the right angles inside of the tent.
I can't really narrow it down any further than that, I'm afraid.