After testing several things in Blender, I think I see where the values in the transform location come from. Bear with me through the description.
Create two objects, arbitrarily move, rotate and scale both in object mode. Select the first object. Transform location shows the coordinates in the current world (global) 3D frame of reference. Parent it to the second. The location values don’t change, but the current reference frame is saved with the parenting info as the local parenting frame (not the same as the local parent’s frame). Take note of the second object’s location, rotation and scale then arbitrarily change them. The first object obligingly comes along. Select the first object; the transform location hasn’t changed (it’s in the local parenting frame reference, which moved with the parent). Change one of the location values and the first object moves – in terms of the parenting’s local frame of reference, not the local frames of either child or parent nor in the global frame. You can restore the second object’s location, rotation and scale to confirm this.
Changing the location of the parent moves it in global space, not its local space.
Think of it as a hierarchy of frames of reference. At the top is global space, then the parent’s local frame, the the parenting local frame, then the child’s local frame.
With that, it’s apparent what the values in the transform location are – they’re the coordinates in the next higher frame of reference relative to the selected object. (Now, how to distill that down to make it a note in the manual wiki …)
I think there were two points of confusion. First, there’s that extra frame of reference for the parenting link. Second, the actual origin (0,0,0) of a local frame of reference isn’t necessarily what Blender refers to as the origin of the object. Before 2.5, Blender used the term center instead of origin, but neither really fits.
That still doesn’t help with manipulating the child in terms of the parent’s local space, though.