I understand that the ring setting of an Enigma rotor changes the alignment between the internal wiring and the letters on the ring. For example, in the diagram below, rotor I has ring setting 2 (B), which causes current entering at position A (the center) to flow through the wiring from Z to J (internal positions) which corresponds to A -> K based on the visible indices on the rotor.
However, we could achieve the same result with ring setting 1 by using Z as the top character, which would cause current to flow from Z->J (internal positions) corresponding to Z->J on the visible indices.
This leads me to believe that the only real impact the ring setting has on the encryption is that it changes the location of the notch (that steps the next rotor) relative to the internal wiring. For plain texts that are long enough to step at least one rotor this will result in a substitution that cannot be recovered by permuting the rotor starting positions alone.
Is there anything else I'm missing?