Arguably that falls into the last category. If you can work for nothing but equity, then somehow or other you don't need the money (right now).

You probably shouldn't compromise much on salary, since plenty of startups are happy to pay market salaries.

The trade-off for startups vs. big companies is really in whether you're getting liquid RSUs (with clear cash value) or private options (with more upside), not so much on the salary side—especially these days.

Maybe the key here is distinguishing equity from actual control. Non-controlling equity in a private company is like buying a bond with no maturity date, relying on the founders' good faith.