Ponies are going to do what they do, based on who they are, their lifetimes experiences, their attitude to you, their calculation of what's in it for them if they do cooperate, and then they apply standard pony deviation and do something else.
Ponies, horses and equids in general are a prey species. The most important skill set is being scared of predators. Courage is secondary, and the blend of cowardice (aka common sense) and courage (aka stupidity) is what keeps them alive. Too scared and they will never put their heads down to eat and will starve. But a brave zebra (I use Zebras for default wild horse behaviour) when it muscles up to a lion, saying "I'm not scared", is lunch.
Obama does lots of weird things and my first assumprtion is fear. If he is scared, bolting is his best survival option. If a predator attacks, get away from where he aims to hit you. That applies to a lion leaping, a man with a spear or some brave hunter with a gun. If you aren't where he aims to hit you, he misses. So you don't bother with direction if you are a flight animal.
Cattle operate as bunch, so they may look before they leap, equids scatter. So they leap first, think later. Joe Back in “Horses Hitches and Rocky Trails” says “There’s that old saying “If you stop to think”: Well, a horse figures why stop to think, might as well do it on the run.” Joe operated pack horses and mules in the Rockies for years as a working professional and knows that horses run, and why.
Bolting aka Running away, is a hard wired, instinctive behaviour. You can't train it away. You can't "bomb proof". I have had an XL Bully attack Obama. He runs. He has run from maybe 15 dogs, 3 lions, 2 LLamas, numerous Railway crossing gates, occasional fishing rods and from apparently, absolutely nothing.