Ammunition issued in combat was almost always AP, the reason being that it gave better penetration in cover material (dirt, sand bags, etc.) and light vehicles than ball. Ball was usually issued only for stateside training.
Ball ammunition, with a lead core, was never issued outside the continental United States. It was used for Statesdide training and guard duty.
While I'm sure that this was true for the people who lived through it, conversations with a Marine who fought in the Pacific from Guadalcanal onwards, and also in Korea, show it was not the case everywhere.
During his time on Guadalcanal, he said the only AP seen was belted, mixed with ball and tracer, and the guys with Springfields and even most of the BAR gunners got regular ball. Said there was some API, but all that went to the aircrews, like SBD rear gunners, etc. Later on in the war, BAR gunners usually got AP, and the "rest of us" got mostly ball, AP once in a while. In Korea, he said he never got ball, it was all AP, but he didn't know if that was a policy decision, or just that they were getting whatever was in the pipeline.
He also said his "basic" load when he carried the Garand was 96 rnds, the cartridge belts he had were 12 pocket, 6 on a side. Also that spare clips in the pockets were very common.
Also, when going into combat, he would grab a bandolier, or two, and reload out of them until they were empty, keeping his belt load intact as long as he could. Because it was easy to lose a bandolier (diving in a hole to shelter from an incoming shell or bomb could separate your from your bandolier right quick, but the belt almost always stayed with you.
He also mentioned that it was a bit difficult to extract the clips from the bandolier, but they were highly motivated at the time, and it didn't pose any serious problem for them. Also why there were so few bandoliers that survived intact, they were almost always ripped by GIs getting the ammo out of them.
I think its best to assume that while some people saw nothing but AP in combat, and ball in trainging, or even vice versa, making sweeping statements about "that's all that was used" in every theater throughout the entire war isn't accurate.