Perhaps think about it this way:
Lets say we invent a tool, it is two poles you put into the ground and then they print out the amount of curvature in the universe between them. And we’ll agree to always place then 10 meters apart.
You’d find that in the hyperbolic version; you would get the same negative reading no matter where you placed the poles (so long as they are 10 meters apart).
Same goes for the hyper-sphere version (except the reading would be the same positive number each time); and for the flat version it would also be true (but the number would always be 0).