AI is requesting access as trial monitors, special or not. Something they are entitled to under law and the principles of a open justice system because access is something everyone is entitled to.
To dismiss this as arguing for "special status" is to make the argument that you aren't allowed to argue for your own rights unless you also spend the time, energy, and money to argue for everyone else's. For example that an author couldn't sue the government for blocking the publishing of their book unless they also sued the government for blocking the publishing of every other blocked authors book. Not only is that not a duty they have, it's not even clear that they would have standing to do so.
It’s also an extremely well established legal standard for important humanitarian trials, covering many decades across every developed nation on the planet.
Saying anything like “oh Amnesty International is just some NGO to be treated same as the general public so who cares” is completely unrealistic and just fails to be relevant in any way.
Also, if coverage were broad and the principles of open justice were respected, thus providing ample records on what looks like an important trial touching aspects of freedom of the press and the disclosure of war crimes, then AI would not be as interested in seeking to monitor it.