The thing is I could actually see that being the rules they have to follow.
(Gotham Central 002)
The GCPD having an employee whose job it is to call in the vigilante would still count as doing it themselves in real life.
I think that a) "stacy" in the comic isn't actually GCPD (they're actually from the bank/coffeeshop/etc next door) or b)they're not 'officially' (like n the books official) the batsignal-er, they're just the office gopher, who happens to know how to work the bat signal
From memory (haven't gone back to double-check) she's an admin girl (possibly a contractor as well) that works in their office. So she isn't officially part of the GCPD department because she hasn't taken the oaths or anything and might be on another department's payroll.
It's very much a hiding behind a technicality situation.
Alright I had a free moment so rechecked the panels with the full explanation of her situation: