In this video from 2016 https://www.youtube....h?v=lA4DbN01q70 Sinclair states that it has been proven surprisingly safe in over 100 humans.
I also recall that he mentioned in a more recent video that NMN has now passed its human safety trial.
In the video you linked to from 2016, Sinclair was referring to the many NR trials underway and the safety of NR, not NMN at the 6:40 mark. This video was posted in July 2016 and the first human trial with NMN began recruiting in July 2017: "Effect of NMN (Nicotinomide Mononucleotide) Supplementation on Cardiometabolic Function". Sinclair's NMN safety trial at Brigham and Women’s Hospital, in Boston, in late 2017.