Smear: NKT is opposed to Rime
Truth: "Rime" is the "non-sectarian" movement within Tibetan Buddhism. The NKT is also non-sectarian. The real meaning of non-sectarian, which the NKT follows, is to respect other traditions and to refrain from criticizing them.
The Dalai Lama says that to be non-sectarian one has to receive and practice teachings from all traditions of Tibetan Buddhism. Because the NKT does not do this, it is often incorrectly criticized as "sectarian" and as opposed to Rime.
As explained above, the NKT believes that the most effective method to gain spiritual realizations is to practice one tradition purely without mixing. Just as others have the right to mix traditions if they wish, and should not be criticized for doing this, so do we have the right to practice just one tradition without being criticized.
By practicing one tradition purely, the NKT is not saying that it is better than other traditions; just that this method works the best for us. As Mahayanists who understand that living beings need to be helped in different ways according to their differing karmic inclinations, we never say that we are the best and that other traditions are inferior. Rather, we respect and appreciate other traditions and refrain from criticizing them. In this way, we are non-sectarian.
As Geshe Kelsang says in Understanding the Mind:
Every Teacher and every tradition has a slightly different approach and employs different methods. The practices taught by one Teacher will differ from those taught by another, and if we try to combine them we shall become confused, develop doubts, and lose direction. If we try to create a synthesis of different traditions we shall destroy the special power of each and be left only with a mish mash of our own making that will be a source of confusion and doubt. Having chosen our tradition and our daily practices we should rely upon them single-pointedly, never allowing dissatisfaction to arise. At the same time as cherishing our own tradition we should respect all other traditions and the right of each individual to follow the tradition of their choosing. This approach leads to harmony and tolerance. It is mixing different religious traditions that causes sectarianism. (Geshe Kelsang Gyatso, Understanding the Mind: an Explanation of the Nature and Functions of the Mind, pp. 161-162, © 1993, 1997, 2002)
Sadly, the Dalai Lama and some members of his Rime tradition do not refrain from criticizing us. No matter how liberal and tolerant they may be when it comes to receiving spiritual teachings from many different traditions and teachers, they are illiberal and intolerant when it comes to the New Kadampa Tradition. It could be argued that it is this behaviour that should be criticized as sectarian and hence non-Rime.