Swap is absolutely NOT a backup to your memory and it certainly isn't in OS X. Swap is just memory on disk and it is quite useful. Why? Because it frees up actual memory. It is something that is heavily used in virtualisation products because it makes far more efficient use of memory than without it. Swap is more like a parking lot where you can park stuff that you don't quite actively use.
That is precisely what is meant with "back up for RAM". Its not "backup" (as in create safe copy), its "backing store", as "storage that acts as the final guarantee for memory". Please read the 'About the Virtual Memory System" subsection carefully in the document that you yourself have linked.
What you are describing is only part of the story. Memory management is not something that is only done by the OS for very obvious reasons. The app knows about its memory, the OS doesn't and vice versa. Therefor they have to work together. That's why apps can use more memory than they need and why they return memory when other apps need it more. And that's also why they are able to swap. The app requests the OS to swap.
Again, you seem to be confused about a number of things. Most importantly, you seem to be confusing physical memory and virtual memory address space (which have nothing to do with each other).
An app on OS X can give the OS certain hints about how the RAM will be used. It definitely cannot request the OS to swap. Nor does it take any active role in swapping (this is done with processor traps or proactively by the OS). Before advising people to read developer documentation you should do it yourself. Also note that memory management on OS X and iOS is different because iOS does not have a backing store and thus iOS apps need to take care of low memory situations themselves.