I have this story!
("It's Better Not to Know" by Rog Phillips, that is.)
The story told in the first person from one vacationing man’s perspective starts off with the world still being unaware of the mysterious Chih jen being newly landed and not yet come out of his UFO in the Nevada desert.
The protagonist describes strange events of others' prescience about himself:
A stranger asking for one turn on his losing one-armed bandit in Reno and winning that one turn – because he knows he will win it.
A gas station attendant in the desert gets a surprise fit of prescience, and tells the protagonist he should get his rear axle repaired now, before it will break later in the day down the road.
But he doesn't -- and it does.
A woman who finds him on the desert (and deserted) roadside, and gives him a ride, tells him she knows she will marry him even though she doesn’t know his name.
Like the other people, she is puzzled by her unexpected insight about this protagonist, and in surprise also lets slip, “I know we are going to be married and remain together the rest of your life, but I don’t know your name . . .”
He later remembers she had said “something unpleasant”. Specifically, her knowing about "...the rest of your life..."
Later near the landing site -- they are in the Nevada desert near the landing site and follow police cars, helicopters and Army aircraft to the site -- the humans experience a loss of time and a memory of an abduction and return. (In 1958!)
His returned memory includes being inside the ship and discussing with the alien his concept of free will. The alien has an "alien" concept of free will, and replies:
“It appears that you are presenting a rationalization of a blindness to the unchangeable future, a device of pretending there are alternative actualities matching your degree of blindness. A projection of the uncertainties in your thoughts into the external reality. You find security in believing you have a choice, every moment, don’t you.”
The alien is distressed and sad at the condition of Earth, humanity, and its illusion of free will.
The experiences of the humans turn out to be their own experiencing some of his prescience.
He knows, and now they sometimes know, what will happen.
“I had thought to bring light and enlightenment but it would be a world of nightmare to this small world that delights in an illusion of uncertainty. The lure of gambling is not the winning, but the uncertainty, the mechanic who knows the stranger is going to be in serious trouble shortly defies the certainty he knows of by a myth of hoping to alter the certainty and is unhappy when he can’t. And that which should be happily accepted becomes unacceptable when the illusion of uncertainty is gone from it. This is a strange corner of the cosmos.”
I will leave off the ending, as Rog Phillips leaves off spelling out any further certainty in his ending.
The author's shock ending is more about how it's no good to slap your forehead and say you should have repaired the rear axle -- or even to wise up and repair the rear axle. 'Cause it's all just gonna happen anyway. It's all already set in, not stone, but the unwinding of pre-set atomic paths that are going to go only this way.
He conveys the infinite sadness of the alien caused by our bizarre planet with no uncertainty and no free will.
The alien Chih jen is not crashed or hurt, and is able to take off and get his sad self off the Earth.
But this synopsis of this unusual story should be enough to jump-start any lost memories of whether this is the story you sought!