Is the Integrity Problem just with Top Executives?

Yes, I would and have signed a code of conduct at several companies. The sigining of the document is somewhat symbolic. But it makes clear that the company is communicating a message on standards of behavior and they mean for you to hear it and abide by it. I do not believe that relying on each person's personal ethics is sufficient. There are far too many variations in individuals beliefs to insure that each person is following the company's standards. As you come to understand the inner workings of a company more competely - particularly their legal situation - it becomes very clear that such ethics statements are an essential defense. It is impossible to make everytone in the company ethical. But it is possible to set the company standard for ethical behavior and demonstrate that rogue actors are a deviation from the company's stance - effectively removing some degree of liability from the company and shifting it to the individual.

I've also seen the code of conduct work well, provided that the Executive team backs it up with actions. Any positive examples of Executives that stand-out as well above the crowd today in terms of their own conduct?

I have no issue whatsoever in signing a code of business conduct and have done so in my current job for several years (we do it annually). It actually makes a good common framework if you feel someone is crossing the line you just mention that code of conduct and that usually ends any questionable conversation/suggestion. Our code goes way beyond lying, cheating or stealing though! I hope we haven't sunk to those 3 things being the common denominator of ethical behavior in business/technology today! We have actually dismissed people (including executives) for code of conduct violations. It is taken very seriously.