Let me repeat again: The keypoint for the two alternatives for the stability criterion is the question: Is the necessary phase inversion (by design !) for negative feedback inluded in the loop gain- yes or no?
1,) In the avove figure, the loop gain phase starts at 0 deg. If this would be the phase of the total loop gain, we would have 1ßß% positive feedback at low frequencies: No stable operational point - the circuit could not work underclosed-loop conditions.
2.)However, assuming that the design is OK, the above phase response tells me that the shown loop phase did NOT take into account the phase inversion at the summing junction. Unfortunately, some books/authors define the loop gain simply as a product of all the elements within the loop - WITHOUT the mentioned phase inversion . In this case, the critical phase shift is, of course, at -180 deg (because the -180 deg from the supressed phase inversion would give the 0 deg criterion - in agreement with the stability limit at 0db and 0 deg).
3.) During loop gain simulation, the program will, of course, consider ALL the phase inversions in the calculation - and, thus, will consider the 0 deg criterion.
Any further question?