Obviously you cannot expect the horse to NEVER have a little jump, but yes a well behaved horse that once a year does a little quick "start" at something is a whole different ballgame from the horse that suddenly explodes over nothing.
"Once a year..."
My contribution to this subject is based on owning a horse that is 24 years old, has been ridden thousands of miles in the last 12 years (I started her at age 12), horse shows, competitive endurance and trail, a half dozen formal "bomb-proofing" clinics, and STILL spooks a minimum of three times in an hour ride.
She is a granddaughter of the famous Arab *Bask, and has multiple lines to show horses, so I suspect genetics have created a personality that is easily worked up and made to prance and short. I read that no one who had ridden *Bask could say they never fell off of him.
When I started with this horse, I read and asked and searched and pulled my hair out trying to figure out how to get a horse to stop spooking. It seemed impossible to me to get anywhere with this mare because by the time I realized something had frightened her I was on the ground. It was like, "Is that leaf floating toward my horse's head...?" BOOM! Super fast twisting heels over head rodeo bucking.
It was impossible to imagine every scenario that might scare this horse and expose her to it. A donkey braying on a farm nearby, someone starting a chainsaw a half mile away, a squirrel, a garbage can, a leaf, her own water bucket. All of these things made her explode. I led her on long walks where I spent most of the time keeping my feet clear while she sprang up and down around me snorting.
Then one day, my mare froze for a second before bucking and I leaped off and calmed her down. Next she froze for two seconds, then three, and then we had something to work with. Once she learned that fear didn't mean death, we were able to make progress little by little.
After six months, the bucking stopped. After six more, she stopped bolting. I rode the spins, leaps and sidesteps at least half of the time for the next several years. At that point after trainers and clinicians and others trying to help me had marginal success, I met some crazy riders that took their horses out galloping and did some real adventure riding. They let me ride horses that made my little mare seem rather tame.
Once I learned how to really ride securely over all types of terrain, these huge issues I had with my mare became non-issues. My horse has become a solid horse for me, and I can get on and ride her out alone into the woods or on a busy road or beach. She will always spook and I can't change that. Now she simply shudders or drops down with her feet spread wide or does a gallop-in-place and then stops.
This is my "easy" ride compared to my other, more complicated mare who is not as spooky.
I appreciate those who try to understand their horses' personalities and motivations, like bsms and others on HF. The horse is never wrong, they have motivations of their own for everything they do.
Books have been invaluable to me and I've learned much more from them than any instructor. I took many, many lessons that didn't help me become a secure rider. What they taught me is to become what I call a "poser," which is someone who wins equitation classes but when the horse spooks violently they fall off or lose control. I also rode a lot of different horses for many years without learning the right things. I've learned the most from real people with real experiences, books, and from the difficult horses such as my mares.