In the first video, Dr. Valter Longo (one of those listed in the cell.com OP study article) says that he tried getting water only fast research backing and could not due to concerns for safety, so he added / created the fasting-mimicking diet and then got going on human studies. Fascinating interview (first video), and the second is a (shorter) TEDx talk.

Valter Longo, Ph.D. on Fasting-Mimicking Diet & Fasting for Longevity, Cancer & Multiple Sclerosis 10-1-2016
( Dr. Rhonda Patrick is great! )

Fasting: Awakening the Rejuvenation from Within | Valter Longo | TEDxEchoPark 12-5-2016