While I am fully in agreement with all of the OP's disgust with vapid New Age adoption of shallow fantasies (and with the practices of our psychotically-religious ancestors), I think there may be another as yet unmentioned (in this thread) source for the adoption by some modern people of the idea that advanced aliens might have been here in the gloaming of the deep past & left knowledge/hints of knowledge.
Forget a global influence. Pyramids are just the natural shape to build a heap of stone (& in any case, haven't I read somewhere that there are fundamental differences between the S. American pyramids and those of Egypt?). Also forget all-powerful aliens.
What if an alien scout ship crashed on the planet around 10k years ago, stranding the small crew on Earth, with no way to rebuild their wrecked engines/refuel? Before crashing they would have sussed that the Indus valley was the most fertile and likely for an advanced civilisation to begin there, and infiltrated the tribes... they were a new tribe that started passing around ideas, which are still buried in the hindu traditions that developed out of those philosophical ideas which could lead to quantum theory... and our species eventually arriving at the stage where we could reinvent the technology they needed to rebuild their ship and get back off the planet! They have been hiding amongst the Indians ever since, waiting for us to get scientific enough to marshall the resources they need.
I don't know if this idea is widespread, but I suspect that I'm not the only one to think of it.... Fritjof Capra's book
The Tao of Physics more or less leads you to that conclusion, and Roger Zelazny wrote a science fiction novel in the early 60s that showed the Hindu pantheon as a bunch of shipwrecked astronauts setting themselves up for a better life among the primitives:
Lord of Light.
By this conceit, Gautama Buddha may have been one of the aliens trying to steer us towards a less bloodthirsty/supernatural philosophical outlook that could speed up our development to a properly civilised species.
I don't believe any of this scenario, but I reckon plenty of New Age "hippies" are on a positive-thinking trip looking for the apotheosis of our consciousness, and this sort of beneficent sky-daddy replacement for boring religions with a scientific spirituality is just the ticket they need. Having been in the tumult and chaos of India, having been penniless and real high for several months while I was there, I can easily see how a large subculture believing in a secret of aliens-among-us could be spreading, completely ignoring the von Daniken nonsense, fueled by spaced out western kids frolicking in the psychedelic disneyland that is India to our naive eyes.

