Potential wells and symmetry in absorption spectroscopy
This is a bit tricky to explain, the way I imagine it is this: In a totally symmetric mode where, say, each bond extends in phase the potential minimum need not be the same in the excited state and in the ground state but it might be so 'accidentally'. All the forces are balanced. In a non-totally symmetric mode, one set of bonds stretches as the others compress so the potential has to be the same in both states otherwise there would seem to be an internal force being generated that would move the molecule, which is not possible.

edit:

Other points are 

(a) The spectrum reflects the change in geometry between states and thus is that of totally symmetric vibrations only, but see (d) below.

(b) the excited and ground state have to have the same symmetry, 

(c) the asymmetric stretch is a symmetric function of normal coordinates, which is what your lower picture shows.

(d) the non-totally symmetric excited state mode need not have the same frequency  as in the ground state, i.e. potential can be wider or narrower. In this case there are selection rules based on the wavefunction's symmetry; both must be the of the same symmetry in the FC factor. The symmetry of vibrational wavefunctions for non-totally sym. modes change with vibrational quantum numbers and it works out that these type of transitions can have $0 \pm2,\pm4..$ transitions only.