We think her concern/excuse is 'legitimate'. = We think she has a 'legitimate' concern/excuse.
It's not clear that the letter is 'legitimate' [='genuine']; it may be a forgery.
He can 'legitimately' [='rightfully'] claim to be the best athlete in his class.
(..) - Thomas Carlyle, . - Tommy C. These are the receipts from '. - And I'm gonna do '. - I'm sorry. I thought it was a legitimate charity. I didn't know you'd get audited. I don't blame you. I blame myself. - No, blame me. - Okay, I blame you. - No, no, don't blame me. (..)1991 TvShow: Seinfeld Title: The Truth Season: 3 Episode 2