re - "Here is an example of a space-time with space and time curvature that has zero spacetime curvature"

It's more accurate to note that this quality of "space curvature" or "time curvature" is a frame dependent quantity and is not inherent to the space-time manifold where space-time curvature is. That is to say that if the spacetime is flat then one can simply change his frame of reference and the space and/or time curvature will disappear.

A more accurate way of stating that would be

"Here is an example where the observer detects space and time curvature that has zero spacetime curvature"