- amongst others, Spotify can continuously stream music; streaming and playing audio from the background is one of the specific types of multitasking Apple explicitly wanted to allow. A direct quote from their documentation: "Applications that play audio can include the UIBackgroundModes key (with the audio value) in their Info.plist file to register as a background-audio application. This key is intended for use by applications that provide audible content to the user while in the background, such as music player or streaming-audio applications. When this key is present, the system’s audio frameworks automatically prevent your application from being suspended when it moves to the background."
- "Any time before it is suspended, an application can call the beginBackgroundTaskWithExpirationHandler: method to ask the system for extra time to complete some long-running task in the background. If the request is granted, and if the application goes into the background while the task is in progress, the system lets the application run for an additional amount of time instead of suspending it." That's how a well-written browser can continue downloading files when in the background.
- there's an execution mode, designed with VoIP clients directly in mind, that allows a piece of software to connect itself to a socket and subsequently wake on demand. That's how a file store-type application could accept and transmit files without having to be kept in the foreground.
- I'm counting this as the same problem as the file stores on a technical level, though I appreciate it much better demonstrates how the alleged deficiency can directly a task that's an upfront promoted feature and a reason that non-technical people will possibly buy the device, whether rightly or wrongly.
So: yes, the request to continue arbitrary task processing may be denied. Yes, the best support is for event based tasks, and it's a simple fact that the number of permissible event hooks is small.
No, that doesn't mean that multitasking isn't supported, or that it isn't 'real' multitasking. Multiple tasks can run, simultaneously. That's multitasking. Your complaint, taking it at its strongest, is that Apple will sanction only certain types of multitasking, which cuts to issues of approval and control rather than technical software issues.