The reason I thought of this was, well I am English and went to an English school =P We had big scarves like that at school (I LOVE the Harry Potter scarves but it just reminds me of school too much!) and the ends were always like one continuous thing. I could never see where / how they made this thing (but then again I was not a knitter back at that tender age even though it fascinated me).
I think they probably had a purl at the "edges" to make seams because they always stayed so well in shape. Maybe they were just pressed well before being wrapped round our necks!