When I was a JW, we all assumed that no one else really proselytized, aside from perhaps the Mormons. If you'd asked me, I would have thought that no one else bothered to preach to others at all. It would not surprise me that a current or recent JW would be convinced that no other organization spreads the word of God on anywhere near the level of Jehovah's Witnesses. It is one of those things that is taught to them, the same as the claim that no other religion has such internal love and unity as they do.
It's not something that your average JW will question or even try to confirm. They just understand it to be true, and that these 'facts' help to demonstrate that they are truly God's chosen nation. It can make it difficult for the person who leaves the JWs. Even after my fade and eventual realization that I was not religious, it never occurred to me that the JWs were wrong about being ahead of everyone else in terms of proselytizing or their sense of brotherhood and togetherness.