How does "The Minister's Black Veil" reinforce Hawthorne's belief that society is corrupt?
I think it is more accurate to say that this excellent short story focuses more on the corruption in individuals rather than society as a whole. There is a sense in which Hooper's act in donning the black veil is intensely personal, and if we look at what he says on his death bed, we can see that, in a sense, it was a result of the sin that he found within himself rather than society that caused him to wear the black veil for the rest of his life. Note what he says before he dies to justify why he will not remove the veil:
"When the friend shows his inmost heart to his friend; the lover to his best beloved; when man does not vainly shrink from the eye of his Creator, loathsomely treasuring up the secret of his sin; then deem me a monster, for the symbol beneath which I have lived and die! I look around me, and, lo! on every visage a Black Veil!"
Hooper insists that he is no monster in this quote, as others believe. He has been treated as such by others because of the way in which his veil reminded others of their own secret sins, and their own "black veils" that separate them from God and from others. His donning of the black veil was an intensely personal action and it was with the aim of being honest before God and humanity. Thus we can say that this story, through the powerful symbol of the black veil, supports Hawthorne's key belief that it is man that is corrupt.