Sorry, let me explain a litter better.
I've seen various cards come out of chests such as Level 5 Weapons and a Level 4 legendary Item...but they don't exist under my Vault. They do however show up as "unlocked" in the Gallery. I guess I don't see why they exist there, but not in my Vault. Screenshots below...
Vault view of Level 5 Weapons.
http://i.imgur.com/O8HdbtY.jpg
Gallery view of Level 5 Weapons.
http://i.imgur.com/FlLqxYH.jpg
In that second screenshot, that Vicious Double Axe came from a chest. Why is it only appearing under Gallery?
Another example here. Level 4 view of my Vault. The interesting thing that contradicts what was said above...is that I have a Level 4 piece of armor showing up in my vault right now. That armor came from a chest.
http://i.imgur.com/FKZxFdt.jpg
Next picture of Level 4 Gallery with a Legendary item unlocked that came from a chest.
http://i.imgur.com/oQaqC71.jpg
*EDIT*
From seeing the responses above, this is still inconsistent. Some items are showing in my Vault that came from chests and are well ahead of my current Challenge Level.