Closed source in this context literally means that they are not released.
The models of Open AI, Claude and other major companies - are all available either for free or a small amount(200$ for OpenAI Pro). Anyone who can pay this, can run private tests and compare scores. So, the public does not need to rely on benchmark claims of OpenAI based on its pre-release arrangements with test companies.
Yes, by uploading the tests to a server controlled by OpenAI/Anthropic/etc