The school or club may be dressing it up as SPIC, where you could claim PIC time, so you are more likely to pay for the hours.
The reality is, outside an integrated course the instructor would be PIC, or you are PIC with a passenger who happens to be an instructor. If the school are requiring the instructor to be part of the crew for insurance, he is PIC, you are Pu/t, and can only log dual time.
I would take the €800 hit. What is the hourly rate like?