In my opinion, Anna's father might have bought the skull, so as to get money from the government to earn a living for him and Anna.

Most probably, he might have been so poor that he had no there option, but to make some money for their survival by saying that he got a crystal skull, which everyone thought was a relic from the last.

He didn't hide it, but was afraid that Anna might tell the secret . So, Anna's father had cooked up this story, which is fake.