Connecting to Cloud SQL Proxy with PDO - google-app-engine

Question

I'm following this tutorial except that I do not wish to use Silex.
I have set up a Cloud SQL Second Generation instance and a local proxy, which I can successfully connect to using SQL Workbench. This is the code I'm using to connect with:
define('DBH_SOCKET', '/cloudsql/project-***:us-east1:instance-****');
define('DBH_NAME', 'testdb');
define('DBH_USER', 'root');
define('DBH_PASSWORD', '****');
$pdo = "mysql:unix_socket=".DBH_SOCKET.";dbname=".DBH_NAME.";charset=utf8";
try {
$db = new PDO($pdo, DBH_USER, DBH_PASSWORD);
$db->setAttribute(PDO::ATTR_ERRMODE, PDO::ERRMODE_EXCEPTION);
} catch (PDOException $e){
echo 'Connection failed: ' . $e->getMessage();
}
echo '<br />';
if($db) echo 'YAY'; else echo 'NAY';
It works absolutely fine when I deploy the app an visit project-***.appspot.com, but the connection fails when I try to work locally.
Connection failed: SQLSTATE[HY000] [2002] No such file or directory.
I know this question has been asked before in various contexts, but none of their solutions are working for me or don't directly apply. I have added this to my app.yaml file with no change in results:
env_variables:
# Replace project, instance, database, user and password with the values obtained
# when configuring your Cloud SQL instance.
MYSQL_DSN: mysql:unix_socket=/cloudsql/project-****:us-east1:instance-****;dbname=testdb
MYSQL_USER: root
MYSQL_PASSWORD: '****'
beta_settings:
cloud_sql_instances: "project-****:us-east1:instance-****"
Why can't I connect locally using PDO when I can connect locally using my SQL client?