432 Hz is promoted, largely by the Schiller Institute, under the name "Verdi tuning", on the argument that Verdi favoured a lower pitch than the French standard of his day. It also falls out of scientific pitch, which sets middle C at 256 Hz — a power of two, which is aesthetically tidy and physically unremarkable. The article notes that the institute's recommended tuning uses a Pythagorean ratio rather than equal temperament, which is a different claim again.
On health, the page does not hedge: it groups the healing claims with conspiracy theories, including the story about Nazi preference for 440 Hz.
For rig work the practical point is smaller than the argument. Retuning A from 440 to 432 Hz is a shift of under two per cent. On a plate or in a dish it moves a pattern very slightly in scale; it does not summon a different geometry, and no measured biological effect turns on it.