Double insulation, = individual insulation of two items that must not come into contact.
An interesting proposal - but where (other than your personal view) does that come from? As BAS has pointed out, that definition would seem to encompass any two (separate) conductors which each had 'single insulation'.
In terms of Class II items, this all becomes a little silly when one realises that a single layer of 'reinforced insulation' (whatever that may be) is an acceptable alternative to 'double insulation'. ... and what about a single layer of insulation which is twice as thick as qould be required to provide 'single insulation'?
Kind Regards, John