In this case, it's probably the International Red Cross
instead of the American Red Cross.
As for the ARC, my Uncle Paul (the Korean War POW I mentioned last week) had some harsh things to say about them, too. He said it years ago, but if I remember correctly, one of the things he described was how the ARC sold cigarettes to GIs that were plainly marked as donated goods from the tobacco companies. The tobacco companies gave the cigarettes to the ARC so they'd give them to the GIs but the Red Cross sold them instead. There were other things he mentioned but that's one that comes to mind. I've heard other old GIs say similar things.