Modify Google Calendar with non-restricted scopes

I have a PHP site using Google API for user login. Some users have creation and modification role on a public Google Calendar. I would like to modify that calendar, through php API, without using restricted scopes, when one of these users are logged and want to add or modify an event.

$client = new Google_Client(); $client->setClientId($client_id); $client->setClientSecret($client_secret); $client->setRedirectUri($redirect_uri); $client->addScope(ALL_NON_RESTRICTED_CALENDAR_ROLES);

After the login I have:

$service = new Google_Service_Calendar($client); $cal = $service->calendars->get("GOOGLE_CALENDAR_ID");

But I have this error:

Google\Service\Exception: { "error": { "errors": [ { "domain": "global", "reason": "notFound", "message": "Not Found" } ], "code": 404, "message": "Not Found" } }

Does it is possible do what I want? If yes, how?