They gave her an option, which was to claim it via a trust.
The very first thing you should do with such a win is consult an attorney, etc.
Since she didn’t use that option, the prize is humongous, etc., they should probably have another option of allowing the winner to stay anonymous for some percentage or fee for which they can compensate with other advertising.
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.