If the pyramid shape were to extend past the surface of the texture, it would look fantastic up until the point that the viewing angle of the surface would cause the pyramid to visibly protrude past the edge, at which point anything extending beyond those boundaries would be lost.
Here's a terrible mspaint example, please ignore my awful consistency, it's early and I've not had any caffeine yet.
In some games you'll see real subdivision surfaces which are even more awesome but somewhat expensive.
I remember being super excited when these features were making their way from software rendering to GPU years back. I would guesstimate a very large fraction of the perceived increase in game graphics have come from these techniques in recent years.
Cool! What games are using subds? I thought they were mostly relegated to offline use due to evaluation cost.
That is the driving force behind almost all real time graphics! Everything from rasterization to texture sampling to transparency, to this occluding parallax example - it's not exactly correct, but close enough that when used appropriately it is convincingly real and fast.