Well, for a start, when you've got a fully developed API.
We recently built a project that used a Backbone SPA for _some_ views, but was primarily server side.
Now we're building a mobile version, and having built the API in the first phase, we've got enough to go on to do it all via Backbone.
Additionally, when developing for mobile you're much more aware of bandwidth restrictions, so the ability to load only what you need becomes useful. When you're flicking through a bunch of pages that use the same view but with different data, an SPA lets you load only what you need.
Now we're building a mobile version, and having built the API in the first phase, we've got enough to go on to do it all via Backbone.
Additionally, when developing for mobile you're much more aware of bandwidth restrictions, so the ability to load only what you need becomes useful. When you're flicking through a bunch of pages that use the same view but with different data, an SPA lets you load only what you need.