Smear: NKT students are advised not to listen to teachers other than NKT teachers
Truth: It is true that NKT students are sometimes encouraged not to mix traditions together but instead to emphasize their own practices and teachings, understanding them to present a complete path to enlightenment. However, this advice is given in the context of non-sectarianism, respecting other traditions and seeing them as also having a complete path to enlightenment.
No one has ever said in NKT classes that you must only listen to other NKT teachers. For example, there are General Program students who choose to attend teachings of the Dalai Lama and they are not told not to.
Ironically, however, NKT students not allowed to attend either the Dalai Lama’s or Lama Zopa’s teachings if they are relying upon Buddha Dorje Shugden. Moreover, FPMT students are strongly advised not to attend NKT teachings and Centers. For example, one person pointed out in early 2009:
I have practiced at both the FPMT and the NKT for over two years. Throughout that time I was in FP. My NKT Centre has known this and I've had frank discussions about it with all involved, including the Resident Teacher. It's never been an issue. They have also known I took my refuge vows with the FPMT. My teacher even offered to start calling me by my refuge name (yes, you guessed it - it doesn't have Kelsang in it). I've also told them that I have attended classes at the Tibetan Buddhist Society (another Gelug organisation), at Diamond Way (a Karma Kagyu school) and at The Institute of Tibetan Healing Practices (another Gelug-based group).
By contrast, I haven't actually been able to admit to my FPMT community that I also attend the NKT, as it would almost certainly cause problems and I strongly suspect I would no longer be welcome there.
In Great Treasury of Merit, Geshe Kelsang explains how we need to rely upon one teacher and one tradition to attain results:
Experience shows that realizations come from deep, unchanging faith and that this faith comes from following one tradition purely – relying upon one teacher, practising only his teachings, and following his Dharma Protector. If we mix traditions many obstacles arise and it takes a long time for us to attain realizations.
This is, however, simply advice to help students make quick spiritual progress. In practice, NKT students are free to do what they want.