Questions on SAW oscillator circuit

Hi, I am trying to understand the circuit below. It is a SAW based 315 MHz oscillator with OOK modulation. From what I understand the SAW is used to stabilize the oscillation. Therefore, if removed the circuit should still oscillate at the desired 315 MHz frequency by C1, C2 and L1. However, when I calculate the resonant frequency, I get a value of 352 MHz. Could someone explain how this circuit is operating? The application note gives a good explanation of the rest of the design but I am still not understanding how the LC resonator part of the circuit is working. Which components combine to give 315 MHz?

https://www.infineon.com/dgdl/AN099....14269b2d590648

I think you have to include C3 's affect on resonance with 50 Ohm load.
If SAW is replaced by cap, it should oscillate just above 315MHz at 320MHz for this application, is how I read it.

Thank you. How do I take C3 into consideration when calculating resonance? It is not in series or parallel with C1 and C2.

Also, in general, the use of SAW or crystal is for stability purposes? One still has to design an oscillator close to desired resonant frequency with C and L components, am I correct?

this should explain better than I can