To give you a quick recap, CNBLUE performed Crying Nut's 'Offside' in 2010 on 'M!Countdown'; the performance entailed CNBLUE singing over the CD version of the song. In other words, it was the original song with Crying Nut's voice and instrumental, but CNBLUE would simply sing on top of it as well as "hand-sync" the instruments.
CJ E&M had previously compensated Crying Nut for the usage of their song, but the issue arose when CNBLUE included the performance in their 2010 Japanese DVD release. Crying Nut claimed that this not only went beyond the scope of the compensation, but also that CNBLUE had provided Crying Nut with no prior notice of the performance's inclusion in the DVD. CNBLUE's said claimed that they did not know what song they were performing until they went on stage and heard the song coming out of the speakers.
With all that's been said and done, it appears that this issue from a complex misunderstanding between the broadcasting stations, entertainment companies, and artists. One can only hope that when the dust settles, the respective rock teams continue to provide the public with great music in an amicable atmosphere.