Can Appian Process Models be exported to Visio or other tools? I would like to r

The rest of that paragraph refers to the ability to use the process modeler:
"Alternatively, the Appian Process Modeler may be used in the ‘Process Analyst’ view to create process diagrams. In the this case that the Appian Process Modeler is used, simple nodes such as the “User Input” node, “Script Task” node or “Sub-process” node may be used to represent complex units in the process, that is, they need not correspond to actual nodes used in the final process application."

In my experience, it has been rare that Visio (or other tool) has been needed. Perhaps I have just been lucky in that regard.

Out of curiosity, what key functionality do the other available tools give your BAs, other than import and export capability?

You are missing the point. As they state using Appian Process Modeler is an alternative to their Visio recommendation. Appian does a lot of things really well, but playing nice with the other BPMN 2.0 compliant process modeling vendors is not one of them. The functionality necessary to be my current (and previous) organization standard for business process modeling are the 2 I have already stated: that they not be stuck in the tool in case it is not used forever; and that it allows BPMN 2.0 XML compliant diagram imports so the BAs can use their BPMN process modeling tool of choice with importing to the organization standard repository. A great value of BPMN 2.0 is ability to use a tool of choice for business process modeling with the ability to import/export when needed as organizational tools change. Visio, Blue Works Live, and other BPMN process modeling tools provide this, and until Appian does as well it can not be used as the organization standard for business process modeling.