Independence is not a binary state. And that's part of the problem. Independence is something you grow into, and I admit that while I am certainly more independent now than I was 40 years ago, there are still lots of people, senior, junior, trainee and staff upon whom I depend. [which raises the question of what is the opposite of independence? dependence? but don't we all depend on something to some extent? But I digress].
Yet tenure committees, hiring committees are all searching for "independence" and evaluating it as part of their job.
A friend, I've got a few, at another university, who sits on her department Tenure Committee got in touch with me. For advice. She's young. She's ambitious, and she's very very good and just got tenured. So she's safe right? Not quite. Here's her problem (with some details changed to protect everybody involved).
My friend & the dept level TC are being pressured by their (very powerful) chair (Dr. VPC) for a number of more explicit criteria for tenure. Dr. VPC wants specifics like "$X" and "# of Big Grants vs. # small grants".
Why? My friend says that it was the (unspoken) rule that one had to get their own money, their own projects for tenure, and that was what equaled "independence". But now Dr. VPC wants more "nuanced" guides, and explicitly stated that "superficial" things (such as independent lab meetings, and publishing without senior collaborators) are not valid. He may truly believe that this is for the Greater Good, and that The World Is Changing, and Big Labs and Big Collaboration are critical, and not amenable to existing standards. I was guessing not. And my friend said not. There is a young faculty, working with the chair, and so we all say "ah". and then we all say "wtf?". It's politics.
While my friend has tenure, she is still young. She is funded now, but making enemies of senior people is not considered a pathway to success. I asked her to think of the biggest wannabe BSD male colleague she's got. I asked her to think "what would he say to powerful alpha-males?". And she laughed (virtually). That doesn't mean it's a wise thing for her to stand up and fight this. I only want to point out that there are many potential responses.
My advice to her was to talk, confidentially, to some of the more senior people on the committee. By and large senior people guard their prerogatives strongly. My last advice to her was: know what the battle you are fighting is.The independence that is of concern here is not the independence of the folks coming up for tenure, it is the independence of the tenure committee to stand up to a powerful chair. And the chair may not even know that.