He doesn't say anywhere that the bit-depth is reduced.
There is the obvious example of a very low level sound that is encoded from a 24 bit original (meaning it can't be from a CD). The MP3 will not have a problem with the dynamic range, but playing back at 16 bits you could end up with silence, which wouldn't happen with 24 bits.
When the MP3 is decoded to PCM it can be done as 24 bit integer, 32 bit float, etc., and with the proper hardware and software this added bit depth can be maintained through reproduction of the sound.
You will loose something (depending on your dithering or noise shaping method of choice) on the conversion back to 16 bit. LIke others, I doubt this is audible.