The business does not own the sidewalk, just like the business does not own the street in front of their business. The sidewalk is the city's job to maintain, so it is the city's responsibility for its upkeeping, not the businesses'.

Unless this was completely on private property (as in, the sidewalk outside walmart), in which case it IS the business' property.

I guess I really need more information -- where was the sidewalk, on a strip of businesses along a city street? a sidewalk in front of a store on private property in the parkinglot (think walmart or target)?