The result is as expected but for the wrong reasons, I suspect it you short out C6 completely it will still show a similar frequency.
What is happening is the dominant frequency selecting component is now C4. Normally, it's value is very large compared to the LC parts you are measuring and it becomes almost invisible to the signal leaving the L and C to decide the frequency. When you make C6 large as well, the inductor starts to look like a short circuit across it and it plays little part in deciding the frequency. What you are left with is an RC oscillator using the comparators inversion and feedback through R4 to charge and discharge C4.
The LC components will still play some role in setting the frequency but not enough to be able to use it for measurement purposes.
Brian.