He's right, but for completely the wrong reasons.
A capacitor doesn't block AC, it passes it -
Or, even more precisely -- a parallel capacitor to ground acts to block AC transmission (shunting it to ground), while a series capacitor acts to permit AC transmission (exclusive of DC transmission).
And, even more generally, the purpose of parallel planes within the PCB is to achieve a low impedance, nevermind the capacitance. In general -- that is, over hundreds of MHz of bandwidth (such as matters for digital and RF circuitry, the domain where this kind of thing matters), the impedance will be up and down, not simply one way or another. The plane helps in achieving a particularly low impedance across the band. Compared with single capacitors, that have an impedance that falls until the SRF, then rises again. (Mind, you still have to be careful when putting together planes and different capacitors: they can resonate against each other and make things worse. PDN (power distribution network) analysis isn't terribly hard, and is cheap insurance!)
To echo the point others have noted: notice this is only relevant at high frequencies. At audio frequencies (up to and including the low ~MHz, where active devices are just rolling off*), planes aren't very important.
*Rolling off, i.e., gain is near 1, and phase shift is large (>90 degrees?). This is a sensitive region, and it doesn't take much phase shift to turn it into an oscillator. That phase shift will arise in the form of lumped capacitance or inductance though, because again, the frequency is fairly low (say, a wavelength of ~100m).
Tim