That would mean, Kagyu lineages, Nyingma and Sakya lineages by itself cannot lead us towards full enlightenment, which is a ridiculous notion in my humble opinion bordering on absurd. If someone were to say why not learn more from other traditions,I would say to them if you have gotten sufficient instructions to be enlightened why the need for excess teachings and initiations?
Hear ye, hear ye!
Lets mix and match and toss up a fruit salad and hope that gets us to enlightenment! LOL
Rime was a movement in reaction to the Chinese Communists' suppression of Buddhism. This is what Jamyang Kongtrul, a very prominent Buddhist master in Tibet in the 19th century and who is credited as one of the founders of the Rimé movement has to say about having to be grounded in one tradition:
"The scholars and siddhas of the various schools make their own individual presentations of the dharma. Each one is full of strong points and supported by valid reasoning.
If you are well grounded in the presentations of your own tradition, then it is unnecessary to be sectarian. But if you get mixed up about the various tenets and the terminology, then you lack even a foothold in your own tradition. You try to use someone else's system to support your understanding, and then get all tangled up, like a bad weaver, concerning the view, meditation, conduct, and result.
Unless you have certainty in your own system, you cannot use reasoning to support your scriptures, and you cannot challenge the assertions of others. You become a laughing stock in the eyes of the learned ones. It would be much better to possess a clear understanding of your own tradition.
In summary, one must see all the teachings as without contradiction, and consider all the scriptures as instructions. This will cause the root of sectarianism and prejudice to dry up, and give you a firm foundation in the Buddhas teachings. At that point, hundreds of doors to the eighty-four thousand teachings of the dharma will simultaneously be open to you."
Source: The Ri-Me Philosophy of Jamgon Kongtrul the Great: A Study of the Buddhist Lineages of Tibet by Ringu Tulku, ISBN 1-59030-286-9, Shambhala Publications