Even if those anecdotes aren't true, isn't the perception of Seattle being a homeless-enabling city likely to make it a self-fulfilling prophecy if it's believe

Even if those anecdotes aren't true, isn't the perception of Seattle being a homeless-enabling city likely to make it a self-fulfilling prophecy if it's believed widely enough? Homeless people in Canada definitely try to make it to Vancouver if they can because of the perception of an enabling local government and mild weather. Shouldn't the city do something to dispel that perception, y'know, such as enforcement of vagrancy laws?