The argument for the Yin is simple -- portals are for people, APIs are for apps. The aperture for apps is much larger, and allows process-based integration. So just like websites are becoming clients of backend APIs, cloud portals (login and provision X, or enter a prospect Y, or measure Z) are becoming clients for backend cloud APIs. And these cloud APIs can service not only the portals, but for companies such as Innotas, deliver true enterprise integration.
The argument for Yang is also simple -- APIs enable the app economy, which has a very different lifecycle than the traditional enterprise application economy. In the latter, things are planned and resources can be planned equally. In the former, we just cannot. Therefore, cloud as a delivery model makes perfect sense for APIs. Now one can choose internal and external cloud, though I lean towards the latter.
Thanks @sramji for pointing me to the Yin and the Yang duality!! You the man! And Helen Whelan for bringing out the thoughts!