As you imply, vibratory sense is lost in demyelinating neuropathies distally very early on. This is because you will affect posterior column somatosensation (position, vibration) before spinothalamic somatosensation (pain, temperature) because posterior column modalities are carried by large fibers. These are the ones that are myelinated. Pain and temperature are mostly (but not all) carried by small fibers, which are not myelinated. Thus, your statement is NOT true for axonal neuropathies.
When you have diffuse demyelinating injury, such as in diabetes, the first place to suffer is where the most slowing of conduction from the demyelination has accumulated, meaning where the path is longest. That is why the pattern is distal, and worst in the toes.
As for why vibration is lost before position sense and light touch, I'm not completely sure. For light touch, there are many different modalities of sensation involved, such as hair follicle position and nociception, some of which is carried by the spinothalamic tracts and unmyelinated fibers. Maybe the reason that position sense goes later is that it involves more area of sensation and larger amplitudes of stimuli.