Actually Koreans and Japanese like to write things in English in a pretty random manner. Most cases, the grammar is pretty off but it happens.
Both will have entire songs in either Japanese or Koreans, but in MANY cases they will have a few lines of poorly grammared English. Sounds like a joke? It isn't.
As for risking an international incident, their government does it for them anyway.
Regardless of it, whether or not it was real (unlikely) or photoshopped by some Korean kid (likely) it shows the animosity between the two sides.
A lot of things don't make any sense.
I too believe that Japan and South Korea need each other because of China and North Korea.
However, South Koreans increasingly fails to recognize North Korea as a legitimate threat thinking that it's some kind of propaganda artificially created by the Americans (funny because they believe all kinds of weird, unfounded, unlikely and sometimes outright bullsh*t propaganda but take things that have a lot of substance and truth and discount it as propaganda) and the Japanese INSIST on claiming a set of South Korean islands in the East Sea/Sea of Japan.
So you have yourself a funny situation. You think it should be a no sh*t, clean and cut arrangement but the truth is stranger than fiction.
The current President is trying to change these attitudes but Japan's actions and attitudes are not helping anyone one bit and the public's protest against everything (and I mean EVERYTHING) the President wants to do doesn't help either.