This is true when housing demand is controlled entirely by how many people live in the area. However, large metro hubs like NYC and London have a larger percentage of the housing supply consumed by rich people who buy part-time housing so they have somewhere nice to crash when they visit once in a while, or so they have somewhere nice for tourists to crash where they can make money off Airbnb. In that context, net emigration does not necessarily rule out a tight housing supply.