Basically the Tibetans threw the Chinese monks out, there was a debate which the Chinese monks were challenged in a philosophical debate and all the Tibetans agree that they lost the debate. Well Zen and other forms of Chinese Buddhism are not really about debate, but we don’t know what school the Chinese Monk was from who was debating. But from that point forward the Chinese influence on Tibet was according to them not great. So I think this is a case of attaining the same ends independently, and also the actual end points are different. Zen Buddhists even though they reject the scriptures for direct experience of enlightenment never claim not to be Buddhists, or to have heretical thoughts, rather in the northern school at least they claim to have no thoughts, which may be worse. At least Dzong Ka Pa does not make that mistake, i.e. go to the extreme of getting rid of reason. But he makes the mistake of getting rid of reflexivity of awareness. So I guess mistakes are inevitable.
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Suggest you read History of Buddhist Philosophy: Continuities and Discontinuities David J. Kalupahana Which identifies the Lankavatara Sutra (http://en.wikipedia.org/wiki/Lankavatara_Sutra) as Heretical in Buddhism, and thus brings doubt about the teaching of Bodhi Dharma (http://en.wikipedia.org/wiki/Bodhidharma) who brought Chan from India and who emphasized the sutra. Thus if this is true, then we can see that both DzogChen and Chan/Zen started as Buddhist heresies. And so that sorta makes sense as to how Chan could go on to reject sutras, as means of access to Enlightenment and develop is own methods that somewhat departed from the middle way as in the Northern Chan.
By the way the Sutra of Hui Neng is one of my favorite books of all time. If you have not read it please do. (http://en.wikipedia.org/wiki/Hui-neng)
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The Platform Sutra: The Zen Teaching of Hui-neng
Ultimately Chan/Zen became the Practice that went with the Theory of Hua Yen Buddhism and was associated with the Flower Garland Sutra. (See The Flower Ornament Scripture: A Translation of the Avatamsaka Sutra
Thomas Cleary) (http://en.wikipedia.org/wiki/Avatamsaka_Sutra)
Personally I like Caodong/Soto Zen (http://en.wikipedia.org/wiki/S%C5%8Dt%C5%8D) better from a philosophical point of view because of its complex dialectics and the deep work of Dogen Kigen (http://en.wikipedia.org/wiki/Dogen_Kigen). But the source of the reinterpretation of emptiness as interpenetration is definitely in Hua Yen (http://en.wikipedia.org/wiki/Huayan_school)which was brought to perfection by Fa Tsang(http://en.wikipedia.org/wiki/Fazang) .
Mipham corrected the mistake of Dzong Ka Pa and defended reflexive awareness in the name of DzogChen. I think Hui Neng corrected the distortion brought into Chinese Buddhism by the Lankavatara Sutra and that is why he is such a pivotal character in the History of Buddhism. The northern school continued on with the mindlessness syntrome while Hui Neng brought Zen back to the middle way.
Anyway, this is the sense I have made out of it all this far. It is really hard to compare Chinese and Tibetan buddhism. It is like the difference between Analytical Philosophy and Continental Philosophy only infinitely more so. The tibetans were great philosophers, who got mixed up in Tantrism and could only extract themselves by developing DzogChen, or taking it from their Bon counterparts. By establishing the Logical nature of DzogChen Manjushrimitra returned Buddhism to the middle way from the extremes of the two truths.
On the other hand the Chinese already had a nondual tradition that was philosophically sophisticated and was at the core of Chinese society and culture. What the Chinese had to learn was first that Buddhism was not Taoism in another cloak. Then once it has separated the two, it had to try to put them back together again, and the most philosophically interesting thought to come out of that was the philosophy of interpenetration. Emptiness suddenly was founded on a positive interpretation of existence rather than merely the a-concept of emptiness.
So the question becomes whether interpenetration as interpreted in the Awakening of Faith in terms of Alayavijnana (http://en.wikipedia.org/wiki/Alayavijnana) is the same as the Ground, or Basis, or Manifestation discussed in DzogChen. The aphorism for DzogChen is Mind is like Space. This is the identification of Existence and Void. But I have not seen anywhere that they say this ground is interpenetrating. So they could be two different states at the same meta-level of standing, i.e. the manifestation meta-level where the Dual Nonduals of Emptiness and Void merge. I would venture to say that interpenetration is how existence looks from the point of view of the Basis, Ground, Manifestation as indicated by DzogChen, and is probably not the character of manifestation itself. Perhaps if someone gets far enough in the two traditions they will tell us someday if the states are the same. But we can clearly see the break with Buddhism in both, and the correction in both that returns to the middle way beyond Buddhism.
Tien Tai on the other hand is based not on an original suttra but a translation that is ambiguous, and seems to identify a nondual middle way between the two truths. In my opinion even though this is going in the right direction it is based on a misunderstanding and so that does not count. (http://en.wikipedia.org/wiki/Tien_Tai)
See also https://docs.google.com/document/d/1KYGitC6DPXPKJs2r_j_iBms6J6cdnk5u_OA1bBQte-w/edit?hl=en_US for permission requests to use book covers in this article.