If your definition of rich is $110k salary or owning $1M in assets (which translates to relatively safe passive income of $40k before tax, according to the financial planning books I read) then sure, you can absolutely achieve it with careful career planning. I don't believe that's what most people would call "rich" though. There are actually people who will tell you that $100k in the Bay Area is "barely breaking it even" (not that I agree.)
I freely concede I could be wrong with respect to directors and partners. I work at a software company and my girlfriend works at a law firm.
I absolutely agree with you that the odds of getting rich by starting a company are low, all I'm saying they're better than the odds of getting rich by other means.