This issue has confused me for years, and I still at this level unable to find an accurate account or even an empirical logic with which I can grasp it. The conceptual logic of this matter, however, exists. Let me explain.
In generative syntax, a finite (tensed) clause TP, which agrees with the subject, is argued to licence a nominative subject. This has been the tradition since 1981 (and probably before). Empricial evidence for this matter is not problematic:
(1) She likes him
(2) She thinks that she likes him
The subject agrees with the verb by virtue of tense T which is finite and consequently license the nominative subject in the clause. This is not the case in infinitival clauses:
(3) To like him would be nice
(4) She seems [to like him]
(5) She wants [him being liked]<br/>
This logic has been lumped up under the notion of Probes in Phase Theory (Chomsky, 2000, 2001, 2008 et seq.). The premise of this theory states that T is a probe which values features on the DP subject. If this T is finite (strong), it values agreement and nominative case feature on this DP subject, otherwise it's defective (e.g., Raising/ECM). In Raising (4) the DP subject had to find another candidate to value its nominative. This cannot be the infinitival to like him, but it should be seems to like him which is tensed. This is why it moves there, or it remerges there. In (5), being liked which is participial has no subject candidate, this is why the DP there is accessed by V which values only accusative (in fact it's v which values it, V is lexical it does not do the job).
There's no problem with this (for me). What is puzzling is the fact this logic is carried over to vP/DP object relation. The object, say Bukowski, in (6) is valued as accusative (replaced by him) due to the fact that v probes it.
(6) Lydia likes Bukowski
(7) Lydia likes him
The verb like in (6)/(7) is dominated by a v giving:
[vP v' [v PROBE [VP [V' {DP GOAL}]]]]
The logic in Phase Theory says that as T probes the DP subject and values its nominative/agreement features, this logic can be carried over to the relation between v and DP object, on which basis?
As far as I know it follows only from something called Virtual Conceptual Necessity, it's like derivative. We derive an assumption of v-DP object dependency from T-DP subject. Is there an empirical ground which could lump up v and DP object apart from this conceptual motivation, because I find it rhetorical in this sense as Postal (2003) argues.