No, it doesn't "depend". Foreigners are prohibited from working in retail. They are NOT prohibited from working in management positions in hotels, restaurants, and other businesses. If you have a work permit like you're supposed to, you can in fact, do work.
If the owner doesn't know how to do it, then the OWNER needs to pay the agency, not you. The law requires the owner to file a TM30 for any foreigner staying at their place.