I can't read that paper (because of the paywall) to figure out how how they determined the cause of death, beyond simply measuring LSD in the body. http://www.erowid.org/chemicals/lsd/lsd_death.shtml says "LSD was listed as a cause of death by a coroner where more plausible causes of death were the injuries received in fights with police officers."

Assuming it were true, it's odd that a PubMed search finds no more recent papers. No matter what, it's decidedly rare. Renee Honaker was believed to have died of LSD overdose. Quoting http://www.wvgazette.com/News/201303090102 :

> Downey said his initial research into LSD-related fatalities hasn't returned very many reported cases. ... Dr. Elizabeth Sharman, head of the West Virginia Poison Center, hadn't researched the case but said it's the first fatality she's heard of in the state.

Later, "It turns out that the drug Todd and Reneee Honaker took was not LSD after all; according to WSAZ, a TV station in Charleston, it was an NBOMe compound." - http://www.forbes.com/sites/jacobsullum/2013/10/21/lsd-did-n...

NBOMe is also a psychedelic, so falls under the general thesis of the OP. However, it's a rather recent psychedelic so cannot be the reason for the prohibition.