Speaking as a person who was a scheduler for three years, what makes you think that schedulers are even allowed to be shoppers let alone assign shops to do themselves? I never saw it happen and never heard of it happening.
It just varies for company and scheduling company. I most definitely was allowed to schedule myself to shops that I was scheduling. It was encouraged. My contract also allowed me to be a shopper for any company. So I guess that is what makes me think its allowed.