What I don’t understand is, if she was contracted by the magazine to take photos, and the magazine had the subject (McCain) appear for the shoot, then why don’t the photos belong to the magazine?
It depends on the contract. Generally speaking, if a publisher doesn't make a specific contractual request to own the copyright, a free-lance photographer owns the copyright to their own work, and sells the rights to use the work for a specified use and a specified number of reproductions. The magazine would own the photos only if the photographer were on staff.
In cases like this all photographs belong to the photographer - period. There is an implied copyright the moment that shutter clicks. The photographer then 'loans' the pictures to the magazine for publishing.
Now if the photographer works for the magazine, or a newspaper (on the payroll) that's different as he's acting as an agent of them.
In the olden days we had 'Model Release Forms', but in reality they were just a formality/courtesy. I think I still have some in one of my old camera bags, they're polly all yellow and brittle by now.