sqlite login only reading last password

I'm trying to create a login which only needs PASSWORD to access. I've got this.

/* Validates the login form data, checks if username and password are provided
@return bool Login form data check success state */
    private function checkLoginFormDataNotEmpty() {
        if (!empty($_POST['user_name']) && !empty($_POST['user_password'])) { return true; }
        elseif (empty($_POST['user_name'])) { $this->feedback = "Username field was empty."; }
        elseif (empty($_POST['user_password'])) { $this->feedback = "Password field was empty."; }
        return false; } // default return


/* Checks if user exits, if so: check if provided password matches the one in the database
@return bool User login success status */

    private function checkPasswordCorrectnessAndLogin() {
        // remember: the user can log in with username or email address
        $sql = 'SELECT user_name, user_email, user_password_hash
                FROM users
                WHERE user_name = :user_name OR user_email = :user_name
                LIMIT 1';
        $query = $this->db_connection->prepare($sql);
        $query->bindValue(':user_name', $_POST['user_name']);
        $query->execute();

        // Btw that's the weird way to get num_rows in PDO with SQLite:
        // if (count($query->fetchAll(PDO::FETCH_NUM)) == 1) {
        // Holy! But that's how it is. $result->numRows() works with SQLite pure, but not with SQLite PDO.
        // This is so crappy, but that's how PDO works.
        // As there is no numRows() in SQLite/PDO (!!) we have to do it this way:
        // If you meet the inventor of PDO, punch him. Seriously.
        $result_row = $query->fetchObject();
        if ($result_row) {
            // using PHP 5.5's password_verify() function to check password
            if (password_verify($_POST['user_password'], $result_row->user_password_hash)) {
                // write user data into PHP SESSION [a file on your server]
                $_SESSION['user_name'] = $result_row->user_name;
                $_SESSION['user_email'] = $result_row->user_email;
                $_SESSION['user_is_logged_in'] = true;
                $this->user_is_logged_in = true;
                return true; }
            else { $this->feedback = "Wrong password."; } }
        else { $this->feedback = "This user does not exist."; }
        // default return
        return false;
    }

So I removed the things related to 'user_name' until I got this:

/* Validates the login form data, checks if username and password are provided
@return bool Login form data check success state */
    private function checkLoginFormDataNotEmpty() {
        if (!empty($_POST['user_password'])) { return true; }
        elseif (empty($_POST['user_password'])) { $this->feedback = "Password field was empty."; }
        return false; } // default return


/* Checks if user exits, if so: check if provided password matches the one in the database
@return bool User login success status */

    private function checkPasswordCorrectnessAndLogin() {
        // remember: the user can log in with username or email address
        $sql = 'SELECT user_name, user_email, user_password_hash
                FROM users
                LIMIT 1';
        $query = $this->db_connection->prepare($sql);
        $query->execute();

        // Btw that's the weird way to get num_rows in PDO with SQLite:
        // if (count($query->fetchAll(PDO::FETCH_NUM)) == 1) {
        // Holy! But that's how it is. $result->numRows() works with SQLite pure, but not with SQLite PDO.
        // This is so crappy, but that's how PDO works.
        // As there is no numRows() in SQLite/PDO (!!) we have to do it this way:
        // If you meet the inventor of PDO, punch him. Seriously.
        $result_row = $query->fetchObject();
        if ($result_row) {
            // using PHP 5.5's password_verify() function to check password
            if (password_verify($_POST['user_password'], $result_row->user_password_hash)) {
                // write user data into PHP SESSION [a file on your server]
                $_SESSION['user_name'] = $result_row->user_name;
                $_SESSION['user_email'] = $result_row->user_email;
                $_SESSION['user_is_logged_in'] = true;
                $this->user_is_logged_in = true;
                return true; }
            else { $this->feedback = "Wrong password."; } }
        else { $this->feedback = "This user does not exist."; }
        // default return
        return false;
    }

PROBLEM: It works, but only with the first password in sql database.

Any solution please? I would thank you so so much :(