Ya know, this says the statues were originally on platforms. The legend is that the statues walked to where they are. The platforms were also the transportation devices?
I think the locals’ answer about how they got to their locations — “they walked” — was just a bit of dry local humor. It has been suggested that they were rocked from side to side (just a little) after they were upright, but I don’t think it’s true, not least because Von Danniken made such a big deal out of it.