defending corresponding squares

I'm currently reading the book "secrets of pawn endings" (from Müller and Lamprecht). One of the exercises (A1.14) gives the following position with the question:

Find all combinations of three adjacent squares (horizontal or vertical) that can be defended by the black king.

The answer given is that black can only defend all vertical combinations of three squares between the 6th and the 8th rank. Though, I do not understand why a vertical combination of three squares between the 5th and the 7th rank isn't possible as well. For example (with the corresponding squares e5, e6, e7):

What do I miss (or is it a mistake in the book?)

White has made progress despite blacks 'horizontal opposition' with 4. Kd5.

But it depends where he's trying to get to.

I ment if white tries to come at one of the squares e5, e6 or e7

I think you're right, though this is an unbelievably complicated exercise to illustrate opposition