BPMN Black-Box Pools in Multi-Pool Models

I recently received the following from a former student in my BPMN Method and Style training:

"I'm trying to find some rules regarding when pools should be shown as a black box with message flows to the pool boundary or multiple white box pools with message flows connecting events/activities within the different pools. From what I have seen, it seems that the multi-pool method can be used when showing interaction between different processes and black box pools are used to show external process participants. Is this correct? Any clarity you can provide on this would be greatly appreciated."
First, the context: Some business processes cannot be modeled as a single BPMN process because the instances involved in different parts do not have one-to-one correspondence. BPMN Method and Style asks you to model that scenario with multi-pool structures, each internal pool representing a single BPMN process, coordinating their actions and states through a combination of message flows and shared data stores. In the examples in class the internal pools are white-box (containing flow nodes) and the external pools are black-box (empty). The question is what is the "rule" about this.

Of course, the BPMN 2.0 spec provides no guidance. My general rule would be simply this: If the second (or third, etc.) internal pool is defined independently of its use in the multi-pool structure, it is better modeled in its own model and represented in the multi-pool diagram as a black-box pool (hyperlinked through the tool or model repository to its definition diagram). If not, it is OK to model it as a second white-box pool in the original collaboration diagram. Whether modeled as black-box or white-box, pools representing internal processes should be labeled with the name of the process, not the organization.