When we copy the NBT (CTRL+Midle Mouse) of an Item Frame the game copy only the item in.
So, We can't copy an item frame with an item in.
edit :
The problem is the hit box of the item is bigger than the Item Frame.
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Issue Search : copy item frame, NBT item frame
Linked issues
Comments

In fact a duplicate of MC-48742 (also NBT data of entities)
Not a duplicate, i think is just a Hit box problem with item in the item frame.

Yes, seeing it.
Confirmed for 14w10b
Confirmed for 14w10c
Confirmed for 14w17a
Confirmed for 14w20a and b.
Confirmed for 1.8.7 and 1.8.8. This is intentional behavior as middle clicking should give you the item inside the frame.
Agreed.
Confirmed. However, keep in mind that item frames are entities and not blocks. Also, relates to MC-48742 and MC-48503