Yes, I don't necessarily agree with that. There are:
class 2 items which must not be earthed (I know you don't like that),
class 1 items which must be earthed, and
items which cannot be earthed - plastic items, e.g. plastic switches.
Exactly - and (forgetting my personal views about the Class II ones!), it is the third (I would think pretty common) group that we're talking about - and, although they don't (by your definition of three groups) have a DI symbol, it would seem totally daft (as well as probably being contrary to definitions) to call them "Class I".
What about metal light switches? Are they class 1?
I think there are a few which are Class II, and are marked as such. However, forgetting those, they presumably
are Class I, aren't they - since they are using earthed metal to provide protection from electric shock?
My Henry vacuum cleaner is marked class 2 but in the third category.
I think the same is true of many items marked as Class II. True 'double insulation' seems relatively uncommon, many/most Class II items relying on 'reinforced', rather than 'double' insulation to achieve their Class II status. That being the case, one of your 'third category' would only not qualify for Class II status if their insulation was deemed to not be sufficiently 'reinforced'.
I suppose that leads me back to my usual question, of whether a 'third category' (nothing to earth) item is actually 'allowed' if it does not have adequately 'reinforced' insulation to qualify as Class II. On the face of it, such an item probably does not provide adequate protection against electric shock - which, the in absence of an earthable metal casing, seemingly has to be provide by adequate double/reinforced insulation.
Kind Regards, John