What actually happens when you swipe an app out of the recent apps list?
I appear to have found the magical search terms that led to some explanations from Google employees. Specifically, I found a couple of different places where Dianne Hackborn explains what happens when you swipe something out of the recent list. The first is a comment on one of her Google+ posts:


  [W]hat specifically happens when you swipe away a recent task is it:
  (1) kills any background or empty processes of the application (see
  http://developer.android.com/guide/topics/fundamentals/processes-and-threads.html#Lifecycle
  for what this means), and (2) uses the new
  http://developer.android.com/reference/android/app/Service.html#onTaskRemoved(android.content.Intent)
  API to tell any services of the application about the task being
  removed so it can do whatever it thinks is appropriate.


She also notes in a blog comment:


  Actually, removing an entry in recent tasks will kill any background
  processes that exist for the process.  It won't directly causes
  services to stop, however there is an API for them to find out the
  task was removed to decide if they want this to mean they should stop.
  This is so that removing say the recent task of an e-mail app won't
  cause it to stop checking for e-mail.
  
  If you really want to completely stop an app, you can long press on
  recent tasks to go to app info, and hit force stop there.  For stop is
  a complete kill of the app -- all processes are killed, all services
  stopped, all notifications removed, all alarms removed, etc.  The app
  is not allowed to launch again until explicitly requested.


So, it looks like the summary is that swiping an app out of the list will first kill all background processes for the app, then use onTaskRemoved to notify the app that the background task was removed. At that point it looks like it's up to the app to decide what happens, so I guess there technically isn't a hard-and-fast rule about what happens to the app beyond that point.