A statement George loves to repeat without practical data to back it up with.
The switching frequency is several 100sKHz at the very least and the output filter does not filter it out entirely. Regardless the filter does not have the effect at audio frequencies that George suggests.
The effect of the filter is to remove the switching frequency, which none of them do entirely. What is left is called 'the residual' and will be a sine wave at the switching frequency. It can't be heard, and because its a sine wave does not interfere with radio and the like. But it is energy, and should be unable to damage the tweeter. So it should be at a low level. The inductance of the speaker itself is often enough that the residual is of no consequence unless the switching frequency is stupid low (and there are no class D amps in production like that).