Confirmed in 14w21b
*UPDATED*
To only describe the spectating, as checking the chest does work.
If you click a chest in spectator mode, it opens the chest, so you can see the contents, but not edit it. With minecarts, you see what the cart sees...
Confirmed in 14w21b
Confirmed in 14w17a
Confirmed in 14w11b
This appears to be fixed as of 14w10c. I summoned an Item Frame with invulnerability, and could interact with it totally normally in creative mode, but in survival I could only rotate, not destroy or remove the item.
Can also confirm it occurs when the display is set to the sidebar
But an enter_block trigger kicks off at 20 fps. Point taken though