I'm an undergraduate linguistics student, and I'm currently reading this chapter by Coon & Preminger (2015) (http://ling.umd.edu/assets/publications/Coon-Preminger-17-SplitErgativity.pdf), which describes aspect- and person-triggered split ergativity as resulting from changes in clausal structure. It's assumed that structural cases are assigned configurationally (i.e., case follows from the specific syntactic position of an argument). The portion of the chapter on aspectual splits in ergativity makes sense to me, but I'm struggling with the section in which the authors describe how "specificity" affects configurational case assignment in nominative-accusative languages.
In this section, they explain that in Sakha (Turkic), specific objects move out of the VP and receive accusative case, while non-specific objects stay within the VP and are 'bled' from accusative case (example uploaded below). They state that this is because the accusative case is assigned configurationally, and it can only be assigned in a position local to the subject and outside of the VP. This explains why the specific object in (12a) receives accusative case while the non-specific object in (12b) does not. (The -*(y) in (12a) indicates that it's ungrammatical to ommit the accusative suffix -y, it took me a few minutes to figure out what that was trying to communicate.)
This makes sense to me, if it's true that accusative case is assigned somewhere outside of the VP. However, this is not an idea that I have ever encountered before. I'm aware of nominative case being assigned configurationally in Spec,TP, but I had always learned in my syntax classes that accusative case was configurationally assigned within the VP (in its complement). But the authors seem to be suggesting just the opposite: (12a) is assigned accusative case precisely because it is outside of the VP, while (12b) cannot be assigned accusative case because it still within the VP.
My question is, assuming a configurational theory of case (since that's what the authors I'm trying to understand have assumed), where is accusative case actually assigned? I had always assumed it was assigned by the Vº, but that can't be consistent with what the authors are saying here, unless I'm interpreting their work incorrectly (which is perfectly possible, I'm still an undergraduate). Any clarification would be much appreciated!
EDIT: The specific term the authors use to describe this accusative is 'dependent accusative'. Is a 'dependent accusative' different from other types of accusative?