Answer: the ScrollView is not working when used as the root element of an XML layout. It has to be wrapped inside a LinearLayout.
Solution then :
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
android:layout_width="match_parent"
android:layout_height="match_parent" >
<ScrollView android:id="@+id/scroll_view"
android:layout_width="match_parent"
android:layout_height="match_parent"
android:fillViewport="true" >
<LinearLayout android:id="@+id/scroll_layout"
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:orientation="vertical" >
</LinearLayout>
</ScrollView>
</LinearLayout>