Isn't it much more likely they were brain damaged in a more permanent way? Religious people who use psychoactives tend to openly praise their drugs much like they praise their gods (think soma, peyote, ayahuasca) - middle eastern mystics didn't do that. And with malnutrition, rampant child abuse and almost no health care, there's bound to have been enough brain damage around.

That is also implied in The Transmigration of Timothy Archer. Or, maybe some of the Nephites returned to Jerusalem with a stash...

And of course, as Risto_Saarelma mentions in a comment further down, it may be possible to attain similar states through mental exercises without benefit of pharmaceutical remedies.