That is wrong, and the differences have nothing to do with human hearing. White noise is flat per frequency - i.e. all frequencies have equal amplitude, but pink noise has equal energy per octave, which will yield a perfectly flat trace if a system is dead flat in response. If you look at white noise on a spectrum analyzer, you will see a 3dB per octave rise with frequency - not something you want to use to measure for flat response.

Because there is increasing energy within each octave as frequency increases (there are more frequencies represented), the energy within each of those octaves is more; 3dB, or twice as much more per octave.

That said, the signal used in home theater equipment and on most test disks is filtered pink noise. It is filtered to have energy in the approximately one octave region straddling 1kHz, and nothing anywhere else in the audio spectrum (except for the different signal used to test the subwoofer levels).

The full bandwidth pink noise on some disks is actually more accurate in determining the real SPL over the entire audio band, but it is also more work to interpret, since it gives really more information than most people need to do something as simple as calibrating a system.

If you use bandwidth filtered pink noise from your preamp to set levels, chances are very good that if you check the levels using full bandwidth pink noise, the results will be different.

In any event, you should never use white noise for testing any audio system unless you know how to interpret the resulting data.