The reason that the structure on the right is not valid because "only the placement of the electrons may be shifted from one structure to another." The figure on the right shows a shift in the placement of not only electrons, but also one hydrogen atom (see attached). Moving the hydrogen atom from C3 to C1 is not appropriate because it involves breaking and reforming a sigma-bond (single bond). In general, you should only move pi-bonds (double & triple bonds) and lone pair electrons for resonance. In other words, you do not want to alter the connectivities between atoms.
A rule of thumb that helped me with resonance structures in organic chemistry was that you should not push electrons onto sp3 hybridized atoms. Doing so would either require you to either (A) break the octet rule or (B) move atoms within the molecule.
Hope this helps