I don't think it is ok to scramble onto a horse that is spooking sideways anymore. But I think it is fine to gallop out on a first ride if the horse is well prepared. I feel safer in a pen of untouched horses than in the company of someone's hand-fed spoiled horse. But at least it is clear which horse would flatten a person, the one already trained to do it
Unsafe feelings happen with the occasional horse that rears up striking or purposefully back with an intent to kick, or fling themselves over backwards or trow themselves at fences where other folks have laid those foundations into the horse. More than unsafe feelings are feelings of sadness and anger that somebody made those horses feel they need to respond that way.

"It's really quite amazing what a horse will do for you, if he only understands what you want. 
And it it's also quite amazing what a horse will do to you if he doesn't." ~ Bill Dorrance