Yes, you are wrong - it's more complex than that.
The signal on pin 3 is important to analyse in order to determine operating frequency. When the output is low, the voltage on pin 3 is determined by R3, R4 and R2 - this is the voltage the capacitor has to discharge to in order to cause the op-amp to flip from being low to being high. Then, when the op-amp output is high, the capacitor starts to re-charge up to a new high voltage. Pin 3 is now a higher voltage because the output is now high and, via R2, it sets a higher threshold (on pin 3) than what it did when the output was low. This is called hysterisis.
The capacitor charges and discharges at a rate determined mainly by C1 and R1 but, if R2 is relatively big it's going to take longer to attain the "new" threshold in order to flip the op-amp output.
This is how they work - calculate the two voltages that could appear at pin 3 and these two voltages are what the cap charges to and then discharges to during one period of oscillation. Then, use what you know about exponential charging of a capacitor via a resistor to fill in the gaps.