What Harry should've asked isn't where the experience was taking place but whether the Dumbledore he was talking to was the model of Dumbledore in his head, which only knows things that Harry knows, or enough of the actual Dumbledore to know things that Harry doesn't know. That is, what's relevant isn't the location of the experience but the source of the information feeding into that experience. That would also be the relevant criterion for distinguishing between, for example, a message from God and a hallucination.

That's like saying is depression real, or is it just happening inside the patient's head?

The correct answer is yes and yes.

'Of course it is happening inside your head, Harry, but why on earth should that mean that it is not real?'

Because... it's not real?

Within the perspective of a fantasy world it certainly can be. It isn't just Harry imagining things. Magic is involved.