To interpret otherwise would be similar to saying a unit of archers could not fire on a unit that is Stubborn because the rules never specifically state that Stubborn units can be shot at. Of course the rules don't state that! If they had to list every situation where something was allowed, the book would be thousands of pages long! Instead, we get a blanket permissiveness; we assume that when the shooting rules say you can shoot at an enemy unit, you can shoot at any enemy unit (barring restrictions, which in the case of shooting includes not being able to shoot into close combat). Likewise, Death Shriek says you can shoot at an enemy unit, we assume that it can be any unit (Also barring restrictions, which in the case of unusual attacks, do not have any firing into close combat restriction). Incidentally Gorblud, could you please point me to the section of the rulebook that states Resolving Unusual Attacks only follow the last few steps of the shooting phase? I couldn't find it in my cursory examination of the rulebook, so I'm just going off what you said.
That said, I do think this rule is broken and should be FAQed. With VC's access to numerous tarpit units, it seems easy and unfair to trap a large unit in combat and then just shriek them down. But even if they do FAQ it, that doesn't mean Gorblud is wrong in his interpretation- there are many times (I saw T10 name one the other day) where GW makes a ruling that quite clearly violates what is stated in a rulebook. I guess it's easier (and saves GW a bit of face) to FAQ things rather than Errata them.
EDIT: If you disagree with this, then please clearly point out which rule is being violated. Saying that other ranged special attacks are not allowed is not an argument, because I'm pretty sure all these other attacks state that this particular attack cannot be fired into close combat, which obviously doesn't apply to Death Shriek.