This post needs to be marked for the extremely delusional stance it tries to argue.
International travel is quite common. You can easily verify what I said. Since its fairly basic its not something anyone would lie about. It should prompt you to question your source (though you can even verify online that EU countries require no visa from US citizens anyways).
Applying for visa is quite different. Most countries do want to see a number of documents from ticket/hotel confirmation to bank statement. For fairs, my company always issues a stamped and signed statement covering expenses of any employee applying for a visa. No one in Turkey, excluding people like, has visa-free travel to EU countries.
There are two factors in refugees travelling to European countries. One is the human factor. When thousands of people bank on your borders you can't just shoot them off. Turkey didn't accept 4 million Syrians to Turkey because they could travel to Turkey visa-free. Second factor is that by international law countries are forced to accept asylum seekers. The 1951 Refugee Convention obligates countries to accept refugees.