After digging around a bit, it was discovered that the remains were from people who had lived (and been buried) at the Erie County poorhouse/almshouse (1851-1913), prior to UB being built.

POUGHKEEPSIE, Dec. 14 The Board of Supervisors of Dutchess County has just returned from an official visit to the County Almoshouse, in the Town of Washington, near the little hamlet of Miilbrook.