Thanks for taking the time to respond, Chris.
Your answer is refreshing. My current approach is using BPMN to communicate business processes, whether they include humans or electronic systems, to the stakeholders in a manner that is non-techy. For instance, even though "Get Payment Authorization Details" is an activity that occurs electronically, I still communicate it as part of the business process. I then may have an Activity diagram showing what the system does to get payment authorization details: "Relay Account Info" --> "Get Account Info" --> "Account in System?" [yes --> "Check Account Status" --> "Status Okay?"...] [no --> "Send Authorization"...].
I'm trying to use UML more for IT than to model business processes. Seems like a logical approach to me!
vinny