As
@Brandon ***********
said, there is a high chance they just want the control. You are eligible for a work permit on your non o based on marriage. It is even less paperwork for the school as they don´t have to provide paperwork to support your visa too. Only the work permit. Thing is, if they can´t control your visa, like in threatening you for example that if you don´t do this and that, they will cancel the visa, they lose that option.
Seeing as they already play that card, I would avoid working for them altogether! Find another school!