Capacitor voltage influence
Have a look at the image on this page. It's one of the representations which are clearer on how the IC works. I'll reproduce the image here:



You can clearly see that the voltage divider is independent for any pin of the circuit (well, except Vcc and Gnd). So the 1/3 and 2/3 voltages are just derived from there, but the actual comparison is done by two comparators, which take the pin 2 and 6 voltages to set and reset the F/F (flip.flop)

EDIT: Just found this diagram from the Texas Instruments LM555 data sheet, which is also quite neat: