I didn't mean to imply that you had to have the culture baked on day 1. But by the time you've moved beyond cofounders and are making hires, you better be well on your way to having it defined. Or you're doomed to wallow in misfits and repairing poor hires instead of moving rapidly.
And I totally agree that the founders drive and define the culture. It's their responsibility to establish it, manage it, and change it, if need be.
I'd actually take an approach of formally defining the culture once it has established itself (and is working well).
But well, there's still too many variables to consider. Personal culture of the founder(s) would be very important in picking the right approach. Although many people would like it to be,I don't see management becoming a hard science anytime soon.