So says an article on the BBC's web site. What they mean by 'most distinct' is the number of specialist genes expressed during the normal functioning of the testicular tissue. So: testes, 999; cerebral cortex 318; the liver, 172 and so on.
At the end of the article it's suggested that the testes have 'more distinctive proteins because of their focus on producing large numbers of sperm without any errors in their genetic code'. I'm not sure I can detect an argument there, but doubtless a read of the original paper would be more informative.
One thing not present in the BBC article, but suggested by a moment's thought, is that this may have something to do with the modern drop off in sperm quality. The more genes expressed, the more pathways that are doing something, and the greater the possibility that exposure to some random chemical — be it industrial or pharmaceutical — will make something go wrong.