The US government has nothing to fear from the Red Cross. If the Red Cross discovers violations of the Geneva Conventions, it will inform the affected government, but stay discreet on the issue against the outside. Keeping access to POWs is a top priority of the Red Cross. The Red Cross is a unique institution among NGOs, the only one named in international humanitarian law, with unique access possibilities (and a unique moral dilemma: access vs information).
On a sidenote, I think the US administration wants to modify the human rights situation with national laws? I don't think there's much of a chance to change Article 3 of the Geneva Conventions. The other possibility to avoid article 3 would be withdrawal from the Geneva Convention but that's totally unlikely, too... The administration would rather add a new interpretation of the GV or introduce yet another combattant status if necessary.