I don't know how they can argue with a straight face that using short-term rent to pay mortgages and leases doesn't raise the prices of real estate. That extra income is (obviously) going to get factored into real estate prices when someone makes an offer on a property. And the people who are using it now to supplement mortgages are going to use that income as a selling point when they try to sell their property - "gets $XXX/day on short-term rentals."
EDIT: typos & minor wording