The AppCompat library is added when you set your min target to something under API level 13 or 14. (HoneyComb or Ice Cream Sandwich) so those apps can use and have an ActionBar (among other things). The support library (v4) on the other hand is required for ViewPagers in anything below API Level 16 (the FragmentAdapters of a ViewPager use Fragments from the Support Library in API level 14 and 15). It's only in Support V13 that the ViewPager Adapters start using the new "pure" Fragments.
So if you want a "pure/non support" Android App, you can go for API level 14, but you might still need the Support V4 library for some things.
For unknown reasons (I'm sure they had some), Google added some stuff directly into the compatibility library (and viceversa) only so sometimes you need it even when you really don't want all the code…