Indeed the distribution of the ciphertext when using Airdrop relies on the authentication made by Airdrop (I think that's why Airdrop requires iCloud to be enabled, but note I'm not sure of that). However the encryption of the ciphertext and the keys used are independant of Airdrop. In the worst case a wrong receiver would be selected, he would have the ciphertext but wouldn't be able to decrypt it.
edit: I think I've wrongly interpreted your question. Are you asking if Core Secret doesn't simply reimplement what Airdrop provides? If this is your question, the answer is no, the goal of Core Secret is to divide a secret between peers, each peer having a portion of the secret.