One common argument against building new market-rate housing is that there is an infinite supply of rich foreigners willing to soak up new supply. One obvious flaw in this argument is that housing prices do occasionally go down even in expensive places.
But even leaving aside this reality, the “foreign buyers” argument is not logically provable, since there is no way of knowing whether there are more rich foreign buyers in San Francisco than in, say, Raleigh or Houston.
Thus, the argument rests on the following chain of logic: 1) we know that there are rich foreigners taking over Expensive City X (but not Cheap City Y) because housing prices are high; (2) therefore, the rich foreigners are what keep housing prices high in City X.
The argument makes sense only when you add the following premise: housing prices can only be high in the presence of huge numbers of rich foreigners. I really don’t see any reason to take this premise seriously.