Population activity in auditory neurons allows rate coding of soundwaves with frequencies that exceed the firing rate limit. Place coding is, however, believed to be the most important mechanism of pitch coding in the auditory system.
First and foremost: hair cells do not fire action potentials. They are analog mechanoreceptors, where the ion channels open and close in response to the 'hairs' (stereocilia) moving along with the sound waves, regardless their frequency.
The secondary neurons in the auditory system convert the analog output to the all-or-nothing spikes; these are the the spiral ganglion cells in the auditory nerve. Auditory nerve fibers are indeed not able to fire at 20 kHz; that's too fast. In fact, frequency following is believed to be sustained at at about up to 1 kHz or so in humans, perhaps somewhat higher in some other species.
The fact that the auditory nerve can still convey signals with frequencies exceeding the limit imposed by the absolute refractory period of auditory nerve fibers is the fact that fibers are not alone; multiple fibers in different refractory states (imposed due to stochasticity) are able to convey frequencies exceeding the frequency following limit. Consider a population of neurons that is activated (fires more) at a certain part of the soundwave's phase, and is inhibited (fires less than baseline) at the opposite phase. These neurons are in different refractory states due to stochasticity imposed by random neurotransmitter release from the hair cells and resulting random firing in the auditory nerve fibers. As a result, some fibers are activated at the stimulating phase of the sound, whereas other are unresponsive because they are in an absolute or relative refractory state. When the second period of the tone comes in, the unresponsive neurons in the previous wave can be excited, whereas the previously active ones are now refractory. The principle of this rate coding is explained in Fig. 1.
However, besides rate coding, there is another mechanism at work in the cochlea, namely that of place coding. Place coding operates by the fact that the cochlea is frequency tuned, meaning that high frequencies are coded basally and low frequencies apically. In turn, even when all neurons fire at the same rate, the brain can nonetheless recognize their place and hence their encoded pitch. This place coding is, arguably, the most important way of frequency coding. The tuning of the cochlea is shown in Fig. 2.
Fig. 1. Rate coding in the auditory nerve. source: Open University
Fig. 2. Place coding in the cochlea. source: Cochlea.eu