My question is: are processes the wrong focus? Given a complex problem domain (for example a payroll system), isn't a physical model of the problem domain itself better than an implementation of processes which are hard to determine and subjective in nature? Perhaps another way to put is to question the degree to which which a payroll system might be built on the back of a series of state machines that are often associated with business "processes".
Perhaps such a complex problem domain is a bad example and it is intended to expose processes in some other context?
This is a great question. Our approach here is that there are certain processes that can be easily modeled and digtized, and others that are not. For those that are not (a complex payroll system), we aim to provide a more "informal" way of managing them. That is, there are a series of steps that need to be made, but you can collaborate on top of these steps in a more informal manner (by commenting, tagging people, uploading documents, etc).
We have found that even in complex processes, there are steps that need to be followed. For the uncertain aspects of that process, it is best to just describe it at a very high level and use the informal collaboration I just described.
Perhaps such a complex problem domain is a bad example and it is intended to expose processes in some other context?