On a typical multi-track recording the cymbals will NEVER reside on a single track. With the exception of the Hi-Hat, the cymbals in a drum kit are rarely spot mic'ed and even if they were, there would still be very significant spill into the other mics. So, you get the cymbal sound from nearly all the individual mics but most particularly the stereo overheads (which of course also contain all the other instruments in the kit). In practise, at the small time-scales we're talking about, a drum kit recording is ALWAYS a terrible mess! Typically we would have: 1 (sometimes 2) kick drum mics, 2 snare drum mics (top and bottom heads) but sometimes only 1, a Hi-Hat mic, a mic for each of the toms and a stereo overhead pair. The distance between the kick mic and the overhead mics is going to be around 6ft, so the time difference is going to be in the order of 5-6ms (as sound travels just over 1ft in a ms). The smallest time difference between kit mics will be about 0.7ms, while the biggest is about 5-6ms (if we ignore the likelihood of a room mic, which will have a delay of around 20ms or so) and of course, we're not just talking about time differences between various mics and the overheads (which all vary between about 2-5ms) but also time differences between each individual mic, of which there'd be a minimum of 5 but probably 8-10. So the recording is a mess to start with and then we use compression and other processors, such as EQ and reverb (with a pre-delay of around 15ms and decay of 1-3 secs) which messes with the transients' shapes and timing even further. So, do you hear this terrible mess on pretty much every rock/pop recording in the last 60 years, or do you hear a generally pretty tight/punchy drum kit? If you can't hear this terrible mess, then how can you hear the relatively minor/insignificant filter ringing buried within that terrible mess?
We're used to talking about nano, pico and even femto secs here and sure, we can discriminate a difference caused by timing errors down into a few hundred nano-secs range but we can't actually hear those timing errors as timing errors, our ears are nowhere near that sensitive. In fact, even with the ideal circumstances, we can't discriminate timing much below about 2ms, we hear it as a variation of phasing/frequency, not as separate events in time and, a drum kit recording is hardly the "ideal circumstances"! The common problem in the audiophile world and even here in the sound science forum, is that we don't consider what it is we're actually reproducing. There is a general ignorance of music itself, of it's performance, of it's perception, of the recording and production of music and therefore of how measurements, the science and tested limits of human hearing actually apply in practise (in terms of scale and context) to what it is we're trying to reproduce!
1. Again, the cymbal itself would be recorded both with a stereo (overhead) pair and multiple mics and it would be spread across both time and space, as would ALL the instruments in the kit and not only the cymbal/s. If you can hear it in the cymbals why can't you hear it in the even more distinct snare drum or hi-hats? You've taken theory and/or the tested limits of discrimination, ignored the actual practicalities/realities of music recording and production and come up with your own theory which sounds perfectly plausible to you and anyone else unaware of the actual practicalities/realities. What you're suggesting is not absolutely impossible but A) Is very unlikely and B) Is typically very undesirable anyway! And C) There's a much more likely explanation you're ignoring. Have you ever heard of a "Sizzle Cymbal"?
Sizzle cymbals are not uncommon and could easily account for what you're hearing, with no need to resort to magic or absolute hearing thresholds. The individual taps of the rivets can be heard quite distinctly under some practical/realistic circumstances, given accurate or emphasised HF response speakers or HPs but often it's quite near the edge of audibility and therefore slight differences in level could cause it to become inaudible or even small differences in sitting position (relative to the speakers) or HP placement.
2. It has been tested, everyday by thousands of music engineers all over the world, for about 50 years!
Additionally, as amirm has correctly stated, there is nothing in real sound which is anything like an impulse used for testing. Sure, there are transient peaks which can be very slightly similar but then real sound never contains ONLY a transient, there are ALWAYS other components to the sound after the transient.
G