With your definition of the open loop gain, G=+1 is the condition to have singularity in a closed loop transfer function 1/(1-G).

But this is not the sole criteria of the loop stability.
Basically, the closed loop transfer function should not have "unphysical" pole.
For more about loop instability, you should refer stability criteria in literature such as Nyquist's stability criterion.

Both of the X and Z loops look unstable with the current gain.