Horses are animals and react to stuff in mostly a 'flight' mode - so even if they 'think' they saw something they didnt like - they're off !!
Even a 110 % bombproof pony isnt all the time and it can be 1/4 of a mile before a horse that spooked and buggers off stops to think about it !!
Give 'em space and work with the rider - if they are worth their salt they will let you know what works for their horse by halting you or waving you past !
Patience is a virtue