Earlier quoted context omitted.
Smart, hardworking people (the same people who might succeed with a startup) can absolutely get rich (in the "don't really need to worry about money" sense, not in the "absurd conspicuous consumption" sense) working for $BIGCORP in their 20s.
How, and over what timeframe?
To compare meaningfully to startup careers, you need to factor in the premium you pay to work at a startup (in reduced wages) and the very low odds of any given startup making its employee equity liquid.
Generally, the difference between the BigCo path to 1MM and the startup path is that, barring dramatic changes in the nature of our industry (which changes would also confound the startup comparison), the BigCo path is reasonably contingent only on your execution. You can fire on all cylinders in every startup you work at and never end up in the money.