Are we sure that the algorithm used to adjust tuning to 432 Hz doesn’t also change the overtones? The study cited by the OP was double blind and used music that was recorded at 440 and adjusted to 432.
The study showed measurable physical differences for 432 tuning that we usually associate with relaxation as well as reported increased enjoyment of the music:
The subjects were more focused about listening to music and more generally satisfied after the sessions in which they listened to 432 Hz tuned music.
One study doesn’t prove anything but to say that 432 Hz tuning is nonsense when you don’t have any proof isn’t very convincing either. An open mind is a good thing.