No, audio compression doesn't filter out high frequencies, that's just what computer audio as a whole does. And I don't think there's enough of those high frequency components in what humans typically record for a cat or dog to notice the difference. As far as compression, the tricks that work on us should work on them.
the early xing mp3 codec famously cut everything off above 18khz, but that was out of spec. :)
instead perceptual audio compression typically filters out frequencies that neighbor other frequencies with lots of power. deleting these neighbors is called perceptual masking and to the best of my knowledge, we do not actually know if it works the same way in animal auditory systems.
>MP3 compression works by reducing (or approximating) the accuracy of certain components of sound that are considered (by psychoacoustic analysis) to be beyond the hearing capabilities of most humans.
-via Wikipedia
This holds true for most other audio compression as well.
Now, it's true that max recording frequency is bounded by sample rate via the Nyquist theorem, but that doesn't mean we're incapable of recording at higher fidelity - we just don't bother most of the time, because on consumer hardware it's going to be filtered out eventually anyway (or just not reproduced well enough, due to low-quality physical hardware). Recording studios will regularly produce masters that far exceed that normal hearing range though.