I'm not an audio engineer by any means, but I'm not sure that sentence makes sense. Mastering is what produces the final audio output - if you take a badly compressed master it's not going to matter if you export it to 16 or 24 bit.
Nor can anyone hear the difference between a 16bit and a 24bit file, all else being equal.
While we don't know the exact dynamic range of human hearing, we do know it to be above 96dB.
Either way, using these 96dB in 16bit requires careful mastering.
With CDs, it is not possible to e.g. make a song quieter than the others in the CD without losing this 96dB range. There's no "ReplayGain" metadata in the discs; the format is aged and not fancy at all.
At 24bit, there is plenty, thus preserving what was in the original recording is possible even with bad mastering.
Lets say the mastering process compresses the recording extremely to a 42dB (8bit) range - outputting that to either 16 or 24 bit will make zero difference. The audio will still have a dynamic range of 42dB.
If we're talking unmastered recordings for archival, yes 24bit is very useful. For final mastered copies released for listening it's completely untrue that 16bit doesn't offer enough dynamic range.
The extra dynamic range helps bypass bad mastering.