This is inherently what the board of directors does. Furthermore, you characterization of the make-up of a board of directors is not necessarily correct. Many (if not most) boards also have independent directors, who many not own a single share.
"There really isn't anything in an MBA that would have anything to do with the job of corporate oversight that a board of directors handles."
This left me scratching my head, my experience was the polar opposite of this comment. In my MBA program the topic of the board came up a number of times in finance and management classes. The board & corporate oversight were very much top of mind issues.
That would be what the board of directors is theoretically meant to do. In practice it's extremely far from the truth, with board meetings being very infrequent and focused primarily on share price and dividends.
This discussion is not really about Google though: Google does actually have a very relevant board of directors with most of them being founders or directly involved in starting large tech firms. Many other companies (Nokia? Microsoft?) are not so lucky.
Interestingly enough on Google's board only Paul S. Otellini (previous CEO of Intel) and L. John Doerr (early Intel engineer and VC) have an MBA.