I'm certain Syracuse University and its trustee's have their exposure covered to the hilt. I presume SU won't be "active" in directing, supervising, instructing, etc. any of the work on site (therefore, severely limiting their exposure). But, rather this will be the daily scope/activities of the hired GC, Construction Manager, it's subcontractors and the like. No doubt hold-harmless, indemnity contracts/agreements will be in place, as well as SU being named as an "Additional Named Insured" under those CGL policies.
Undoubtedly, the policies, CGL, Worker's Comp, etc. are enormous from a premium standpoint, and clearly figured into the job bidding, etc. New York State's labor laws are very strict when it comes to falls, etc. from any heights, as LL 240 & 241 basically places "absolute liability" on all of the parties, except the employee/injured party. If something horrible were to happen, SU certainly will be sued and then file a 3rd party impleader against the responsible party/parties, etc. In NYS you can not sue your employer directly.
SU's main exposure comes from a pure premises standpoint and whether they have fulfilled its obligations/duties to makes sure (as the landowner) to keep the grounds clear of any relative hazards, etc. and its responsibilities as the premises owner to conduct routine type inspections and/or "sweeps." Both "constructive" and "actual" notice will play a role in any defense of this principal exposure.