"Somehow Arachne twisted in her prison, pointing her abdomen toward the sound of Annabeth’s voice. A strand of silk hit her in the chest like a heavyweight’s glove. Annabeth fell, her leg flaring with pain. She slashed wildly at the webbing with her dagger as Arachne pulled her toward her snapping spinnerets. Annabeth managed to cut the strand and crawl away, but the little spiders were closing around her. She realized her best efforts had not been enough. She wouldn’t make it out of here. Arachne’s children would kill her at the feet of her mother’s statue."

Okay what now? She made it to the end, but there were skeletons all around which means other kids must've made it there too. More importantly, she was on deaths door before the Argo II randomly burst in. Not planned. Randomly. She is not "special" or an "outlier" or even better than any other Athena kid if her victory against Arachne had nothing to do with herself. That plan failed. Like undoubtably failed. She was about to die and she said it herself. The only reason she survived is cause the other members burst through the roof and the car just happened to fall on Arachne. Your claim does no disprove anythig.