ive heard about this several times yet never personally experienced it, just as asheras
what i can say is that, sometimes, inventory items can occupy the same inventory slot. a few times, i have managed to break my inventory in a manner that would show my inventory as full, numerically, however with 1 or 2 visibly empty slots in inventory. your inventory is in fact filled, but the game believes multiple items reside in one "slot" consider a list numbered 1-100, that accidentally puts 2 variables into say line 55. when you reach line number 99, youll have 100 variables, yet line 100 will be empty.
to rectify this inventory issue, you need to manually move each item to a different inventory slot, kinda like those sliding number puzzles, essentially moving the empty inventory slot around until you reveal the slot containing 2 items.you will know youve succeeded because after moving the item in the offending slot, a new item will appear in the same location instead of the slot being empty. the number of items in your inventory will not change, but the empty, unusuable slot will now be gone and an item previously believed to be gone will be staring at you with a green flashing outline.

i would not be the least bit surprised that the TR inventory, or ANY inventory can experience this issue- however i have only observed this phenomenon in the main player inventory. this is what i believe to be the cause of the "item wasnt in TR bank until i removed things" scenario
my suggestion is to completely empty your TR cache before you give up on an item