Exactly this. As a "boss" I'm part of the team. My guys CC me on shit because they trust me and they value the 25 years of experience I have in our field. When shit goes down, it helps that the boss has been in the loop and has had at least the opportunity to weigh in before things go off the rails instead of being brought in after the fact to do damage control.
At the same time, I recognize that this only works if I'm treating this information flow as simply that. I usually skim most of the e-mail I'm CC'd on for potential issues (which I'll talk to people out-of-band, rather than in direct response to the e-mail) just to keep a general idea of where things are at. That's my job as a manager.
As a counterpoint, I've also seen managers who get CC'd on everything take that as an opportunity to micro-manage.