Quartz Crystal and Resonance Frequencies
You are thinking too deeply about this. Consider this: -



It has the same formulas as your question does (the parallel one re-arranged slightly, but the same) and, because the capacitance (around the loop) is now fractionally less than for the straight series capacitance scenario (because the two capacitors are in series), it has a resonance impedance peak slightly higher in frequency.

That is all that is meant by the parallel resonance - it is a high impedance state and reflects that at the terminals.

I think you are trying to impose a different meaning to resonance in your question.