The word "is" has absolutely no bearing on whether or not an apostrophe is used to indicate that a noun is possessive. Possession = ownership/belonging to. In your sentence, you refer to whom is at fault, the man, therefore, the fault belongs to the man, or it is his fault, or he owns it. Without the apostrophe, the noun "mans" is plural, BUT, the correct way to write the plural of man is "men". Either way, with or without an apostrophe, "mans" is incorrect. That's why it's "man's", because you're referring to a single man having the fault for what theoretically could have happened or has happened. Technically, your sentence could be correct using either the singular or the plural form of "man", but both need the apostrophe:
man's fault men's faults
Notice that when the singular man becomes plural men, the fault also becomes faults. This will not happen in every case; it depends upon the context.