The amygdala is deep inside the brain, and there's no way of messing with it without invasive surgery. So no, this patient didn't go under the knife just to get rid of his manageable fear of spiders. NewScientist reports that the 44-year-old businessman was suffering from sudden seizures caused by sarcoidosis. This rare condition can cause damage to the brain, and it was messing with the left portion of his amygdala.
Once it was removed, the man's fear of spiders was gone. In fact, he went from being afraid to kill spiders by hand to actually wanting to touch and observe them close-up.
But the patient wasn't suddenly fearless. He still had his old fears, like public speaking. It's possible that the part of the amygdala that was removed was responsible for sudden, panicked fear responses (the spike in adrenaline that the patient would normally experience upon spotting a spider) but not more general fear responses (like a fear of being humiliated while speaking to a crowd).
In any case, researchers won't be jumping to carve out brain matter to test the theory -- even for more severe phobias. But since a fear of spiders is so common, they might be able to keep tabs on future patients undergoing the same surgery. Maybe some of them will have arachnophobia, too -- and maybe they'll also be cured.