You are absolutely correct and kudos for being the first to mention it here. It's obvious from the scriptures that James headed the early church (he spoke last -- i.e., the concluding remarks -- at the first council and sent Peter on an errand). The early church and early secular historians considered James the leader of the early church. The bit about Peter being the head didn't come about until more than a century later.
Incidentally, here is an interesting site. It was well-accepted in the early church that James was the half-brother of Jesus. Pope Clement I (a contemporary of the apostle John), Eusebius, Pope Leo the Great, and the Council at Trullo all recognized James as the "brother after the flesh" of Jesus. So did Josephus and several secular historians in the second century. The idea that Jesus and James weren't half-brothers is preposterous and is something on the order of historians 2,000 years from now concluding that JFK and RFK weren't brothers. This ossuary, assuming it's authentic, merely confirms what the early church believed.
Either way it is not likely that the relics of a leading bishop like Saint James would be just abandoned in some obscure box. Much more likely they would be acknowledged more solemnly and venerated or distributed in the following generations. This ossuary containes bones of some other James.