Dzogchen, or rather the Dzogchenpa, is a part of Buddhism as long as you use the Buddhist methods, even if it is "only" Anuyoga.
Since the first vehicle, according to the sgra thal gyur, is the vehicle of gods and men, are you stating that when a Dzogchenpa uses the methods of vehicles of gods and men they cease to be Buddhist?
I prefer to think that the Dzoghen practitioner can make use of all methods without regard to whether they are Buddhist or non-Buddhist. If you want to go to a kirtan, go. If you want to go to a Catholic service, go. If you want to go to a prayer meeting, go. If you want to dance with dervishes, go. If you want to attend a sweat lodge, go. If you want to hang out with a shaman, go, If you want to experiment once or twice with Ayuhuasca with a Brazilian shaman, go ahead. If you want to take peyote once or twice with a Mexican shaman, go ahead. If you want to spend time among Shaivite Sadhus, go ahead. If you want to hang out with Bonpos, go ahead. If you want to hang out with Brahmins, then like the Buddha himself, go ahead. Likewise, if you want to practice shrakvayāna methods, then go ahead.If you want to take refuge, and get a nice Tibetan name, then go ahead. If you want to practice Mahāyāna, then go ahead. If you want to take bodhisattva vows, then go ahead. If you want to practice the six levels of outer and inner tantra, then go ahead. Do you as Dzogchen practitioner have to do anything of these things? Nope. Should you criticize others for doing these things? Nope. What is indispensible for a Dzogchen practitioner in the tradition of Chogyal Namkhai Norbu? Ati Guru Yoga and that is all. Other teachers of Dzogchen will see things differently.