As far as I can see, the best ways to become this is are: (a) be an early employee of a company that grows large enough; (b) get your own company acquired (a subset of case 1); (c) meet the right people early on, especially at a young age; and (d) act entrepreneurially within an existing organization's management, which, depending on the health of the organization, may entail more political talent than productive talent.
That list might be how people assume it happens, but it doesn't reflect reality.
Most early employees never make it anywhere near management if they weren't management employees to begin with (and with venture-funded companies, those usually get replaced; Steve Blank wrote about this I think). Ditto for getting your company acquired (how many acquired YC alumni ended up quitting right after acquisition? something like 99%?). Meeting the right people also doesn't have as much to do with it as you'd suspect - a lot of CxOs are found through searches, and may come from companies in a completely different sector of the economy. As for entrepreneurial drive, that's the reason we're all here reading HN instead of being content with working for an "entrepreneurial" manager.
I recommend reading Sharon Voros' The Road to CEO - it describes the typical public company's executive officers' background pretty well. The basic idea is you have to work your way up the management chain of command and build up a solid resume (spending time at a prominent business consulting shop apparently can act as a short-cut for this). Personal qualities related to making good first impressions seem really important at the high level - the author spends a couple of chapters on things related to grooming and appearance. I don't run in CxO circles, but that seems an accurate impression from the senior management people I've encountered.
Bottom line seems to be you need to get into management and work and charm your way up.
It's true that my impressions are based on all I've known about the backgrounds of execs I've been impressed with, rather than a proper survey / random sampling. Perhaps the 80% come from more mundane middle management backgrounds; I don't have enough data to tell.
I like that you made a distinction between large and extremely profitable companies, because large companies often still pay their CEOs extreme salaries even when performance falters.
Case in point, Robert Nardelli at Home Depot made $123.7 million, excluding stock option grants, over 5 years from 2002 to 2007, while the company's stock price faltered. He was essentially fired and still got a severance package of $210 million. (http://en.wikipedia.org/wiki/The_Home_Depot)
Obviously there's a small number of people for whom this will happen but I'm pretty sure most corporate execs make >$200k