Mysql – PHP: Can’t access to MySQL server on a different server via PDO

I'm trying to connect to a offloaded SQL server offered here. It says that I should connect using the internal IP 172.16.0.51.

I installed nginx and PHP (php5-fpm, php5-mysql) on my VPS. phpinfo() works, too.
However, when I try to connect to the server, I get the following error. I tried connecting to the server using its external IP, but I still get the same error.

SQLSTATE[28000] [1045] Access denied for user 'myuser'@'AAA.BBB.CCC.DDD' (using password: YES)

AAA.BBB.CCC.DDD is the IP of my VPS, not the server's. This is strange because I did not specify this IP when connecting the server.

Here is the PHP code I use.

try {
    $dsn = 'mysql:host=172.16.0.51;dbname=myuser_mydatabase;charset=utf8';

    $db = new PDO($dsn,'myuser','mypassword');

    $db->setAttribute(PDO::ATTR_ERRMODE, PDO::ERRMODE_EXCEPTION);
    $db->setAttribute(PDO::ATTR_EMULATE_PREPARES, false);
} catch (PDOException $e) {
    echo 'PDO error: ' . $e->getMessage();
    exit;
}

What am I doing wrong here?

EDIT: FYI, user myuseris the default user I was given when I signed up for the offloaded SQL. I checked that it has given all grants to all databases. I also created a new database and user through cPanel, and granted appropriate access. I still cannot get this to work. I get the same error.

EDIT2: I added my vps's IP address to the list of allowed hosts from cPanel, but this did not solve the problem, either.

EDIT3: Please see my answer.