Actually, even in the PHB1 this was fairly unambiguous, albeit not exactly clear.
A burst has a particular size, which determines which targets are included. In chapter 4, it says: "A close burst power allows you to target creatures or objects within the indicated number of squares from you in all directions." This also refers to p. 272, which essentially repeats it. Only the example is in 2d, which is reasonable given that that's the normal scenario.
So, for bursts at least, it's pretty clear - what matters is distance from origin square, and that can be counted as usual - i.e. vertical distance counts too.
Blasts are a little more confusingly formulated simply since there is hardly any formulation at all beyond the 2d examples. What is said is that it's an area a specified number of squares on a side; that is most reasonable the specified number of squares on all sides - vertically included, particularly given the way bursts work.
So, you could make the argument that bursts& blasts are undefined, but you'd be hard pressed to make the argument that they're actually flat - it certainly never says that, and for bursts it's particularly hard to argue that they shouldn't be cubes.
So, if you're arguing as a form of personal enlightenment, then there's ample scope for elaboration here. Practically, however, given the text and trying to be consistent pretty much means you need to be using cubes; WotC's staff generally confirms that (although early on they gave a few confusing answers).