I’ll take a wild guess at a couple feasible answers as to how this happens, being a civil engineer.
Bridges are not a static, stay in one place vertically object, especially during construction. Falsework and girders move and sag as the deck is poured/loaded. Wood falsework crushes/compacts, etc.
The precaster/manufacturer for the prestressed concrete girders (as they appear to be, but steel girders are similar) fabricated something incorrect, which allowed the girders to sag further than calculated as the bridge deck was built or the girders did not have enough camber built in originally to account for this. Girders sag as the bridge is loaded with steel and concrete comprising the deck.
During deck construction the deck was loaded improperly, depending on the type or skew of a bridge deck loading during pouring of concrete has to be maintained at specific rates and angles depending on the design. If not the deflection in the bridge may be off side to side or front to back for various reasons.
Someone messed up a calculation on the sag when setting girders and forms.
Someone messed up when surveying which resulted in the 1” error. With the lack of emphasis with most contractors, local and state governments to have properly educated technicians, workers, engineers and foreman (because they cost more) I find this to be the most likely situation. Properly educated, trained and licensed staff cost more than hiring bodies off the street and attempting to train them as has become popular in recent years as labor markets have tightened.
All that said, a design would not typically be set right at a clearance limitation. A factor of safety, say 6”, would be far more common IMO to account for unexpected movement during construction.
