I tried to activate / deactivate plugins till I found that Shiba Media Gallery realy makes this option in my Media Gallery. But I received Shiba Media Gallery with my theme so maybe there is some modification or combination of features which make this option.
I tried to find out where the problem arises. With "classic" editing is everything OK. Issue comes only in Quick Edit mode. So probably in 3rd case I used Quick Edit without even realizing it :/
I made screenshots during this test. You can find them at http://prajvit.pche.cz/polylang/ if you want.