This myth is especially common among feminists and arrogant men.
It is extremely rare to find a person in Russia who is desperate to leave their country, but as always, those who are are, are the ones who make the news, hence getting attention which contributes to this myth.
As a matter of fact, many women who join internet marriage agencies are not even willing to leave their country, but are just scammers without serious intentions who get a high off of having men come and spend money on them, wine and dine them, etc.
One of the ways of doing this is to make you think that other people are worse off than you and would give anything to be in your shoes.
And of course, bad news sells better for the media and its advertisers, since people like to believe that others are worse off than they are and would give anything to be in their shoes, to keep themselves motivated in their current situation in life.
I have heard that in Saudi Arabia, the natives see Americans there who came on a spiritual pilgrimage to Mecca, which they consider the spiritual center of the world.