Coming from a different country and hiring culture altogether, we go for trustworthiness and hard work. We don't hire overly specialized people, because we prefer rational decision makers that can wear different hats over corporate drones. We also don't believe in behavioral interviews, since we know people can fake them.
We have honest, transparent, and sometimes politically incorrect conversations, to uncover core values and integrity. This is how we weed out corruption and laziness from self disciplined work environments.
In the end, what makes a company grow sustainably is not just hiring good professionals (their knowledge will grow obsolete in 10 years), but hiring contrarian, humble folks tirelessly committed to learning and getting things done, even when no one's watching.
In this light, I believe you can find A players both hiring for culture fit and hiring for culture growth. It's indistinguishable, as long as you set the bar high for honest self driven career ambition. In the end, most skills can be learned if you're constantly challenging yourself, even more so with internal LMS training.
What I have seen though, given you mentioned Adam Grant, is that openness should correlate with giver reciprocity profiles. Even when this is encouraged, this is not necessarily the case.
I have seen hard working folks leaving open organizations and startups due to having to deal with fake givers (takers acting as givers to their managers and decision makers).
Cultural frameworks do little to detect these false positives.
There's also an ivory tower component that seems to happen after a company executives grow comfortable after a good company gets large enough.
I like Netflix approach to culture as a framework (http://www.slideshare.net/reed2001/culture-1798664).
Red Hat has self discipline sewn at its core. This makes for a nice environment, where you work with smart people. But, leveraging on these open principles, it should avoid drinking its own kool aid, and keep working to absorb and learn from other work environments and corporate culture experiments.