Fasan, the reason you are getting TRUE(1) returned everytime is because the PHP manual states that TRUE is returned when "mail was successfully accepted for delivery". I would interpret this as the server is accepting the message because it is in the correct format and follows the RFC rules, etc.
After the PHP script has finished executing, the mail server will then try and send the message and hold it and try again for a period of time if it is unsuccesful in finding the recepient.
Do you have access to error logs? They may be able to shed some light or you could try contacting the web admin.