I keep seeing people say that LEDs are three times as efficient as HPS as a grow light. Is there any basis for this? if so, is 300W worth of LEDs really as good as growing plants as 1000W of HPS? I'm aware red and blue LEDs are used, but HPS also has lots of red and blue wavelength components.

HPS are intended to have high efficacy for human vision - have most it's energy in orange, in the wavelength range human eyes are most sensitive. So it mean it does not radiate much in deep red and nearly nothing in blue.
So the "efficacy" as a grow light depend, what colors are needed and how much the HPS radiate there.

So if the blue and red are the only necessary colors, the LED may have, indeed, better efficacy then the HPS.
But then much higher efficacy would come from specialized MH lamps (mainly the blue part).

What i suspect are lot of lies there from grow lighting distributors - based what they claim for terrarium lighting, when try to sell the same fixtures.

I do not know much about indoor planting, but what i know, each phase (photosynthesis, flowering,...) need different colors, but there my knowledge end, so i cannot help much more here.