This is only true if you have no debt. Even in your low-end example you need a net worth of 250k, which is a non trivial amount of money for most people. And I would still call it naive, it's just not enough.
Financial independence to me is, having other assets than your time which will pay for your most basic needs. Living in a van probably means doing a lot of stuff by yourself, which requires a lot of time.
I would disagree with your financial independence definition though. Basic needs threshold is much lower than 'comfortable' living. The traditional definition of financial independence is not having to work if you don't want to. What that looks like (the sacrifices you make) depends on the person. Maybe to be financially independent you are cool with a $500/mo apartment and Ramen... or maybe that means a mansion and a bunch of supercars. Either way, if you're dependent on a job or someone else, you aren't financially independent.
Certainly you can find people who would feel miserable with that amount of money, and people who could thrive on a small fraction, but it would give most people a freedom that very few ever get.