I came up with an example. Say you care about two bits. You can then have the values 00, 01, 10, and 11 (ignore two's complement for now, so that the maximum level is 11, or 3 in base ten). If you take those bits and add two extra bits onto them, so that you now have four bits, XXYY, where XX are the ones you care about and YY are the extras, then the maximum level will be 1111. This technique is essentially what taking 16 bits of CD info to create 24 bits of information does. If you then shift these to have 0XXY, you have lowered the output by one bit (the max level is no longer 1111 but is instead 0111), but the original information -- the XX bits -- are still there. You've just gotten rid of a Y bit, which you made up anyway. Thus, you've not lost any real information for this shift.
In actual practice, it's more complex. For instance, I believe that data is stored in two's complement, which means that 11 = -1 and not 3 in base ten). Also, the link was talking about "1.5" bits; I'm not sure to what the "0.5" bits refers.