Of course, the core internet nodes are not connected by old phone lines, but most of the edge nodes (consumers) are.
Worldwide, DSL is less than half of all fixed lines. Denmark has decent fibre networks, and cable TV, but i haven't found any numbers for usage.
Statistics from http://www.oecd.org/sti/broadband/oecdbroadbandportal.htm
Unity Media advertises fiber connections.
Of course, the core internet nodes are not connected by old phone lines, but most of the edge nodes (consumers) are.