Local management of a banking subsidiary should understand and manage its risk profile, and should have access to information about Basel II implementation in its jurisdiction.
Taking a step back, I think it is also helpful to remember that a number of the home-host issues pertaining to Basel II are actually variations of long-standing challenges faced by bankers and supervisors in the context of cross-border banking. That is, many of the issues under discussion are not necessarily new, but just made more complicated by the framework.