Can foreigners really be responsible for driving house (and other) prices up all around the world?

As I keep seeing it everywhere on country subreddits: Mexico, Spain, Serbia, France, Georgia, Turkey… Everywhere locals seem to think that they cannot afford to live in their home towns because of AirBnBs and foreign tourists / rich foreign retirees/expats.

But with the exception, perhaps, of selected central boroughs of popular cities where short term rentals may indeed raise accomodation costs, surely this cannot generally be the case everywhere. If all these foreigners move TO a place they also move OUT of another place thus reducing the demand for goods and services there. But prices are rising everywhere be it Toronto or London or Mexico City or Malaga.