I did not look into his claims about road accidents but given that Walker misrepresents and so much of the research (and sometimes falsifies it) on sleep, I would not be willing to believe such claim simply based on him saying this in the book.
As far as I remember he cited peer reviewed articles. Anyway a quick search turned up this:
https://www.cell.com/current-biology/fulltext/S0960-9822(19)...