There is a "scientific" basis for that, though I would phrase it slightly differently.
The facts:
"44100 Hz 16-bit PCM" ("CD quality") is just enough to reproduce the total range of sounds, low to high and quiet to loud, for all practical music listening experience, but there isn't much to spare.
- Human hearing has a range of around 100 dB between "threshold of hearing" and literally "deafening".
- 100 dB is around the maximum dynamic range for 16-bit (a little more with good dithering).
- Digital audio hardware uses integer formats (usually 16-bit integer, or 24-bit integer), so 0 dB is an absolute maximum limit.
- Each "bit" in linear PCM encoded audio is equivalent to 6.0206 dB range (about 6 dB).
Whether your recording peaks at -6 dB or -0.000001 dB does not really matter. You are still achieving full 15-bits dynamic range. "-3 dB" is the mid point within that range. However (and this is important), the closer to 0 dB you aim for, the greater the risk of accidentally clipping and causing permanent damage.
(In professional audio studios, recording is done in "24-bit integer PCM" format, and a recording engineer will typically aim for a peak recording level of around -20 to -12 dB. The bottom (quietest) couple of bits in 24-bit AD converters are just noise, so a peak level of -20 dB gives them a practical range of around 18 bits, which is about 108 dB and loads of headroom.)

