The scenario you described is not uncommon and will likely occur more often as organizations move toward more matrix management structures. Especially in large, complex institutions you'll notice that interdisciplinary teams will be created to address specific issues. Who manages these groups? What portion of team members time is spent on activities outside of their own cost center? Depending on who has ultimate responsibility for the work of the team, where do the dollars come from to support these initiatives? These are all important questions and reflect the interdependence of various departments and their role in solving problems and improving care delivery through integration.

I agree with Lowell about the increasing organizational complexity we're seeing with matrixed management. I would say this is not that uncommon now, particularly in regards to your example with a clinical research department and a clinical care division reporting up to the same VP - this is a unique feature of teaching/research hospitals, and our organization has a similar approach in terms of directorships and funding streams.

Actually, I think it's important to view the reporting structure as different from the accounting structure - the organization saw fit to put the two directors on "equal" footing managerially, and in terms of reporting relationship. How their funding is sourced may very well be more complicated, but because a department is non-revenue generating, I wouldn't necessarily classify it as "lower" in the organizational structure. Each department has their own budget targets, and must manage to them as their funding sources dictate.