What's really annoying is when you turn on the CC subtitles and someone speaks a foreign language. The on screen subtitle gets covered with an unhelpful "[speaking Japanese]"
Languages are handled differently in truly multi-lingual media. Watch _Invasion_ for a good example (the first season is amazing, but we didn't care for the second). There, the audience gets subtitles for everything, so viewers often know more than the characters do. There's a beautiful sequence in the desert where two men, unable to understand each other's language, pour out their hearts to each other, and - unwittingly, and across a cultural chasm - share the same hopes and fears.
There's a third way of handling language, which I hardly ever see: the characters on-screen understand each other, but the audience doesn't. The _Star Wars_ by-play between R2-D2 and C3PO is the most accessible example. This is engaging because viewers have to fill in the blanks to infer what one or more of the characters have said.
You might prefer that everything be of the second type, but keep an open mind! The creators probably had a reason for making the choice that they did.
They aren't complaining about closed captions failing to translate foreign speech.
They're complaining about the specific instance where the show/movie has English subtitles for that foreign speech already built in and showing on the screen, and when the closed captions show "[speaking Japanese]" it overlays the translation that the filmmakers intended the viewers to receive, preventing them from experiencing the filmmaker's artistic choice.
For a particular example, it is my understanding that the movie "The Thing" is thoroughly spoiled right at the beginning if you speak Norwegian.