How about if I run them both through a compressor and set the output gain to -inf? They'll both have the exact same sound of silence

. I'll take my reward in all twenties, please.

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Seriously, though, you're right; they won't sound the same.
But to address Rokket's point, they will have similar sonic attributes to them if you flatten them both to pancakes. This doesn't mean they will sound the same, but they will sound far more similar than they would otherwise. This can be true on a couple of counts; first the fact that dynamics are a property of music, one of the "dimensions" of the recording. Much like height, weight or hair color are properties of the human appearance. I don't know just what Rokket looks like, but if you Photoshop our pictures so that we have the same height and weight, we'll look a lot more alike than we would otherwise, even if our physical attributes otherwise are quite different.
Second is that it's difficult to squeeze the shit out of a recording without throwing the general frequency balance off in favor of the midrange. It can be done, and the best MEs can disguise that problem very well, but the very laws of physics and design of our human hearing conspire to force the issue somewhat. The majority of the RMS energy in virtually any recording lies in the midranges; you take too much out and you'll find it rather difficult to obtain the obscene -9dBRMS. Leave too much of it in and the Fletcher-Munson-style response curve of our ears will accentuate the mids that a spectrograph might otherwise tell us are not bumped.
There is a third factor that assists the mids; the preferences of producers and broadcasters for mixes that don't require an audiophiliac response from the playback system to sound good. If a mix depends too much on the very high end or very low end to sound good, it won't sound so good on an office Musak system or a cheap car radio. This is related to the whole "get it to sound good on an NS-10 or Auratone" theory of mix balancing. While it may get a mix to make sense in all playback environments - which is fine - it also can tend to homogenize the sound somewhat by limiting your canvas.
G.