Google Drive API - Transfer ownership as delegated admin - google-api

Question

I am trying to transfer ownership from a normal user to a delegated admin user which has both the Drive service privilege and the Data Transfer privilege, which is required according to the documentation.
I'm trying to do this on behalf of the delegated admin user.
The reason for this is, that I want to make sure that every file that gets created by any user in our domain, will transfer its ownership to one admin user.
So I have an (offline) access token and refresh token stored in my backend. I use the Push Notification service from the Google Drive API to respond to new files created by users in my domain using this (stripped down) code:
$client = new \Google_Client();
$client->setAuthConfigFile('client_config.json');
// This is the access token json for the delegated admin user.
$client->setAccessToken('{access_token_json_string}');
$drive = new \Google_Service_Drive($client);
// This is the file created by the user. It has two permissions: The user is the 'owner' and the admin user is the 'writer'
$fileId = 'XXX_XXxXXXXxxXXXxxX';
// this is the admin user's permission id, of role 'writer'. This is the one I am trying to change to 'owner'.
$permissionId = '1234567890';
// I've tried setting all values, but that doesn't help
$permission = new \Google_Service_Drive_Permission();
$permission->setId($permissionId);
$permission->setEmailAddress('admin#domain.com');
$permission->setValue('admin#domain.com');
$permission->setType('user');
$permission->setRole('owner');
// Both 'put' and 'update' raise the same error
$drive->permissions->update($fileId, $permission->getId(), $permission, array(
'transferOwnership' => true
));
The response I am getting:
Error calling PUT https://www.googleapis.com/drive/v2/files/XXX_XXxXXXXxxXXXxxX/permissions/1234567890?transferOwnership=true: (403) Insufficient permissions for this file
Note that all other API calls work properly, so the access token is valid. There's also no option available within Google Drive itself to transfer the ownership (as being the admin user). Transferring it from the normal user to the admin user works as expected.