It's also not true technically. Safe is relative. People died and people fainted all the time...they were just far enough away that you didn't really hear about it.
I am in my 40s and the distances that I would ride my bike as a 10 year old are shocking when I consider my own 10 year old riding them. This is because I have more stories loaded into my subconscious about how dangerous it is. Has it always been dangerous? Has it always been safe?