I'm not making things up, I'm not a teacher and you obviously know how it works.
What you say sounds correct according to my friend, and I obviously got the wrong end of the stick. He told me that many lessons do not have a teacher, I assumed these are covered by another teacher, but as you say it's obviously someone who just sits in the classroom?
My friend has told me that he is covering several island schools as a supply teacher, the wages are too lucrative to turn down. Add this to the wages of the absent teachers, it's not inconsiderable.
Since you know more than I do, as I'm only passing on pub talk, perhaps you could investigate and report back?