No, they do not say that because they do not think it.
If anyone has said this they were expressing their own view, which everyone has freedom to do, but it is not a view taught within the New Kadampa Tradition (NKT).
Ven. Geshe Kelsang has said that the Dharma practiced in the NKT is pure because it comes from Je Tsongkhapa’s teachings. However, this is not the same as saying that the NKT is the only pure tradition of Buddhism or that other traditions do not have pure Dharma; and he has made this clear on numerous occasions.
What is pure Dharma? According to the ancient tradition of the Indian Buddhist monastery of Nalanda:
The Dharma is pure if it reveals the entire path that leads to enlightenment, presents each point unmistakenly, and has been handed down in an unbroken lineage from Buddha Shakyamuni.
Any tradition of Buddhism whose teachings possess these characteristics has pure Dharma, not just the NKT.
You might also be interested in this recent response to a Tricycle Magazine article: A RESPONSE TO: The One Pure Dharma: The New Kadampa Tradition is controversial—and growing. Why?
I think this quote from Geshe-la when interviewed for Tricyle is very helpful:
“Of course we believe that every Nyingma and Kagyupa have their complete path. Not only Gelugpa. I believe that Nyingmapas have a complete path. Of course, Kagyupas are very special. We very much appreciate the example of Marpa and Milarepa [in the Kagyu lineage]. Milarepa showed the best example of guru devotion. Of course the Kagyupas as well as the Nyingmapas and the Sakyupas, have a complete path to enlightenment. Many Nyingmapas and Kagyupas practice very sincerely and are not just studying intellectually. I think that some Gelugpa practitioners need to follow their practical example. But we don’t need to mix our traditions. Each tradition has its own uncommon good qualities, and it is important not to lose these. We should concentrate on our own tradition and maintain the good qualities of our tradition, but we should always keep good relations with each other and never argue or criticize each other. What I would like to request is that we should improve our traditions while maintaining good relations with each other.”
Also on other occasions Geshe-la talked about whilst he was still in Tibet he shared a place of retreat with a Nyingma lama. He said they engaged in their own retreat practice and tradition, but sometimes would talk and relax between sessions. Practising in harmony and with respect.
Lastly of course in Modern Buddhism Geshe-la writes:
“Today we can see many different forms of Buddhism, such as Zen and Theravada Buddhism. All these different aspects are practices of Buddha’s teachings, and all are equally precious; they are just different presentations.”
You may not find this appropriate to publish but. …Here is the detail Geshe-la gave of his own relations with practitioners of different schools before coming to England. It is clear he felt no superiority towards them, only respect.
“In my class in Sera-Je I had some friends who were from a Nyingma monastery in eastern Tibet. Their daily practice was Nyingma, and no-one was unhappy about this. They had complete freedom. We never had any problems because the abbot gave complete freedom for individual practice.
Although most of my family are Gelugpas who rely on Dorje Shugden, some of them are Nyingmapas. My younger sister married a Nyingmapa Lama from western Tibet from a renowned lineage, he was called Ngora Lama. They had many children, and I visited them frequently, sometimes he and I would do puja together. I would do Dorje Shugden puja and he would do his own practice. We had a very good relationship until his death in Mussourie, India. Now his youngest son and my sister are living in Manjushri Centre in England.
When I lived in Mussourie I had many good friends from the Nyingma tradition, one of whom in particular was called Ngachang Lama. He was an old man, a lay practitioner; one winter he and I did retreat in the same house. In between sessions we talked Dharma, each talking about our experiences. His oldest son would often invite me to his house to do puja. Also, I was often invited to do puja at houses of other Nyingma families. I was so surprised to hear the Dalai Lama and others saying that Dorje Shugden practitioners and Nyingmapa practitioners are like fire and water!”