mmm, you're thinking the right thing, its just le chatlier doesnt always work; it happens to work with temperature and volume changes, but not pressure changes due to addition of a gas. and when one model doesn't work, you go to a more advanced model. which in this case is looking at K.
So K by definition is equal to [A][ B] / [C] for the reaction C(g) <=> A(g) + B(g) when its at equilibrium right? We also know that K at a specific temperature is a constant, which means it will NEVER change, unless you change the temperature.
So lets take the system at equilibrium. (that is Q = K) If you add a gas that won't react with the system, theres no change [A] [B ] or [C] since they're all equal to n/V and adding an unreactive gas changes neither the number of mol of A,B or C or the volume of the container. This means that Q is still equal to K. so theres no equilibrium shift.
We can use this idea to think about volume changes as well. at V1, at equilibrium K = (n(A)/V1 * n(B)/V1) / n(C)/V1. This simplifies to n(A)*n(B) / n(C)*V1. Now if you increase the volume of the system and make it V2. Q = n(A)*n(B) / n(C)*V2. V2 is bigger than V1, so the denominator of Q is bigger than the denominator of K. to make Q=K, you need to make the numerator bigger. which means that n(A) and n(B) must increase. hence the reaction will move forwards with an increase in volume. and this agrees with le chatlier, who says that if you increase volume, you decrease pressure, and the system tried to increase the pressure by moving forwards. and because le chatlier requires less calculations, you use his principle instead.
edit: awks i wrote [B ] without the space, and half my post became bolded;; also i should really learn how to use latex;;;;