Yes, your right in being sure that I would agree with you.Yes I agree too. And on that basis I'm sure you'll agree this is a single phase load: ... Despite the fact the socket it's plugged into (represented by the red line)is this:
Asa I've said, if a load has only two 'terminals', hence only sees the pd between two supply conductors, then, from the POV of the load, there is no meaning to the concept of 'phase' - so there can't be more than one of them!
Kind Regards, John