From what I read, she does want to claim it in the name of a trust but they are telling her she can't because she signed the ticket in her own name and in order to claim it in the name of a trust, the name of the trust would have to be on the ticket. I think she didn't realize that when she signed it as most of the advise you see is to sign the ticket right away.
Right. So she should be able to pay some to get that protection now.
But truthfully I think the states that force every winner to be named may have it right. There is surely insider fraud and the best defense against that is to have the winners named publicly.
Other rich people are almost always known and there is no reason that lottery winners should have special privacy.