That's actually a famous paradox - http://en.wikipedia.org/wiki/Ship_of_Theseus
These bridges were intended to be temporary, whereas stone or metal bridges are intended to be permanent. You are comparing apples to oranges.
The new bridge and the old bridge are actually the same bridge, just made with different materials.
One references location ('the bridge that crosses the river over there'), the other pertains to the physical composition that makes every thing unique (the bridge made of those specific fibers).
It'd be like claiming the different people that inhabit the same house over the span of 100 years are all the same people, because they're all humans. They're all people, and they all inhabited the house ('the people in that house'), but they in fact possess different unique identity.
"How many gas stations are there in _your city_?"
"How would you determine how much rain falls in Washington State in a day?"
There has been a mayor of New York since the mid 1600s, though the individual fulfilling that role has changed regularly.
Similarly, there has been a bridge on this stretch of gorge for some time, though the expanse must be replaced regularly.
It's more like a house blown over in a hurricane. It gets rebuilt, but the land and foundation and some other infrastructure might be re-used --it's still not the 'old house' --it's the re-built house.
If it was the same family or if they shared a few genetic markers that distinguished them from other peoples in the area... then you could say the same people had lived at ________ area.