Tom is correct-I'd add "if the third or fourth finger lands on a note not in the key of C major, ON THE G STRING" it is considered a "half" position.
In answer to your direct question about C on the G string, remember that first finger C results in fourth finger D, therefore the position is "whole," D being in the key of C Major.
The big "why?," who thought this up that is, probably has to do with that feisty Simandl guy, who probably ripped it off from sombody else.
Crap, now I want to know......