There exists a fiduciary duty to act in the best interest of their owners (shareholders). There is no law prohibiting locals from buying up Carrier stock and reversing the actions, but to date, that has not been done. Customers can only vote with their feet (wallets). In this case, if all of CNY quit buying Carrier units, it would not seriously impact the company and may only help to drive the wedge deeper between the corporation and city.
That in no way prohibits SU from obtaining another AC supplier and adding the comment to their marketing. Hopefully, the modifications are sufficient for eliminating Carrier's naming rights, only time will tell.
For the record, I do not support the Carrier decision, only providing analysis. I want Syracuse to thrive, it is my hometown and I will love the place.