What determines whether an item/block with an inventory can be stored inside a shipping container?

[PrincessRTFM]

I was looking for a way to, essentially, use the shipping container to hold something that will itself hold my items. My first thought was Thermal Expansion's strongboxes or satchels. Those are both forbidden, but TE's energy cells aren't. At present, buckets work fine, and so do the handful of modded tanks I tested. When I tried using a vanilla shulker box, it not only was accepted, it also started storing items inside.

What decides whether I can put something with an inventory inside the shipping container? Is it just "anything that exposes a standard inventory capability" and TE's stuff doesn't actually do that? Is there some other restriction?