The Dzogchen’s tradition’s founding myth (Garab Dorje, Uddiyana, etc.) has been the subject of much skepticism, and not only from Western scholars.  Eighteenth-century Tibetan historian Sumpa Khanpo asserted that, contrary to what the tradition claims about its own origins, Dzogchen actually began when a Hindu sadhu came to Tibet pretending to be Padmasambhava and teaching Vedanta, claiming all the while that it was a form of Buddhism. Earlier on, in the thirteenth century, Sakya Pandita claimed that Dzogchen had been influenced by Chan, a view that would be repeated in our own time by Giuseppe Tucci. For what it’s worth, John Reynolds rejects all such criticism on the grounds that it is never supported by any evidence, though he does not admit that the traditional history is equally lacking in evidence. For myself, I find intriguing hints that Dzogchen may have some relationship with Kashmir Shaivism. Here I believe there is documented evidence to make such a hypothesis seem at least plausible.
- Time period. If we rely on verifiable sources (rather than on unverifiable assertions), both Kashmir Shaivism and Dzogchen arose in the closing centuries of the first millennium A.D. This is a better fit chronologically than the idea that Dzogchen was influenced by Chan.
- Literary form. In both traditions, the founding texts take the literary form of a dialogue. In Kashmir Shaivism: “The Tantras are usually in the form of a dialogue between Shiva and Shakti. Shakti asks questions and Shiva gives the answers.”  In Dzogchen: The fundamental tantra consists of “a dialogue between Sattvavajra, who poses the questions, and Buddha Kunjed Gyalpo, synonymous with Samantabhadra, who answers them.” 
- The mirror analogy. Both Kashmir Shaivism and Dzogchen make repeated use of the analogy of a mirror. From Kashmir Shaivism: “In the same way as the mirror underlies everything in the reflection, so God as Consciousness pervades everything reflected in it.”  From Dzogchen: “A master may show the disciple a mirror and explain how the mirror does not judge the reflections arising in it to be either beautiful or ugly: the mirror is not changed by whatever kind of reflection may arise, nor is its capacity to reflect impaired.” 
- Initiatory experience. Both traditions stress the importance of the master’s transmission to the disciple. In Kashmir Shaivism, the master initiates the disciple with Shaktipat. In Dzogchen, the master initiates the disciple with Direct Introduction.
- Consciousness. In both traditions, the central focus is on consciousness, and in particular on pure consciousness.
In a later article on “Kashmir Shaivism and Dzogchen,” John Reynolds notes that both arose around the ninth century: 
Kashmiri Shaivism, as a distinct movement separate from the earlier forms of dualistic Shaivism based on the Shaivagamas, certainly arose with the Shiva Sutras of Vasugupta in the ninth century Kashmir, if not before. Have we a synchronicity here? This is precisely the era when Dzogchen was developing and spreading in Tibet among both Buddhists and Bonpos.
Sam van Shaik makes the case that “Buddhists would have had the familiarity with Tantric Saivism.”  He does qualify this, though, by stating that he doubts that any putative Indian ancestors of the Dzogchen texts will ever be found:
By the time the mahamudra and margaphala teachings were brought to Tibet, no trace was found of the forerunners of the Great Perfection texts, which has since led to doubts over their Indic heritage. Though there is little doubt that most of the texts in the canons of Great Perfection scriptures originated in Tibet, Indic models may well have existed at one time.
 See part III of John Reynolds’ The Golden Letters: The Three Statements of Garab Dorje, First Dzogchen Master (Ithaca, New York: Snow Lion, 1996).
 Swami Shankarananda, Consciousness is Everything: The Yoga of Kashmir Shaivism (n.p., Australia: Shaktipat Press, 2003).
 Chogyal Namkhai Norbu and Adriano Clemente, The Supreme Source: The Fundamental Tantra of Dzogchen Semde Kunjed Gyalpo, translated by Andrew Lukianowicz (Ithaca, New York: Snow Lion, 1999).
 Abhinavagupta, quoted in Swami Shankarananda, Consciousness is Everything: The Yoga of Kashmir Shaivism.
 Chogyal Namkhai Norbu, The Crystal and the Way of Light: Sutra, Tantra, and Dzogchen (Ithaca, New York: Snow Lion, 2000).
 John Myrdhin Reynolds, “Kashmir Shaivism and Dzogchen,” http://www.kamakotimandali.com/blog/index.php?p=1272&more=1&c=1&tb=1&pb=1.
 Sam van Shaik, “The Early Days of the Great Perfection,” Journal of the International Association of Buddhist Studies, vol. 27, no. 1, 2004, pp. 165–206.