Capacitance divider of Colpitts Oscillator
The key thing to note about the Colpitts circuit is that it's not a pure capacitive divider, it's a resonant circuit containing two capacitors in series, as well as an inductor.

At the resonant frequency, and for a limited range of component ratios, the circuit can be redrawn into an equivalent circuit using (amongst other things) an autotransformer, with the turns ratio having the squared form as described (maybe with C1 and C2 swapped, not sure, several people think so). Outside the range of relevant ratios, the equivalent circuit includes things like negative capacitance, which is obviously non-physical. 

Does this restriction to a limited range invalidate the general conclusion? No, because a Colpitts Oscillator will only work within a restricted range of values. You cannot arbitrarily set C1 to 1% of C2 and expect it to work.