@hightor,
Sometimes knowing 'nothing' about the business the corporation is engaged in is actually valued on a corporate board. Several seats on many corporations boards are given to business people with no background in that particular business.
It serves a good 'check' on conducting business in general. Often those who are directly involved in a particular industry are less able to think how things may work outside that industry.
Often just a general knowledge of business, management, operations, etc or knowledge gained from other industries is worth quite a bit. Things like how Six Sigma used in manufacturing at Toyota has now made it's way into the business world (in modified forms of course).
Sheryl Sandberg (from Facebook) is on the corporate boards for Disney and Starbucks for example.