Smallish companies often leave a lot more freedom for their developers, but you'll most likely also be missing a lot of things you've gotten used to (highly automated CI/CD, teams "responsible" for each part of the system etc)
Given that private companies with over $1B in revenue actually exist while examples of "[companies] that values programming and real productivity" are yet to be forthcoming, the parent post is using the metaphor correctly and the finance world is not.
As a perhaps incomplete or shoddy heuristic, smaller startups tend to focus on productivity and moving fast.
The correlation I see is big companies have processes that kill productivity, though I did work for a big company that was able to avoid it for a long time (new leadership did end up killing productivity right before I left).
And for what it’s worth there was no correlation with “agile”. I’ve seen good and bad agile.