Personally, I believe her. However, there is another sinister possibility not researched (AFAIK); someone placed the kid there in order to let the eagle kill her.

As a 3-year old Svanhild Hartvigsen was carried away by an eagle 5th of June 1932, in Leka, N Trøndelag. She still remembers the terrible bird trying to kill her.

200 people participated in the search, they found her baby shoe at the bottom of a cliff where they knew a sea eagle nested. 3 men climbed up to find her, apparently dead, and there is an audio recording with one of the climbers in the national archives.

Sources:
http://www.nationen.no/2010/11/15/rovdyr/svanhild_hartvigsen/havorn/6274004/
http://www.vg.no/nyheter/innenriks/artikkel.php?artid=10011259
http://no.wikipedia.org/wiki/%C3%98rnerovet_p%C3%A5_Leka

The story was controversial among ornithologists in Norway, because there was politically a great campaign to preserve Norwegian wildlife. Some maintain that the 19kg girl could not have been carried 1700 metres from where she was picked up, but given that she remember seeing the eagle flying towards her, and then waking up on a stone ledge in the cliffs, it is little reason to doubt her. Since the people were in church, there’s no reason why the eagle could not have carried her portions of the stretch, until getting her near the nest.

Hartvigsen died 81 years old in 2010.

“AN EAGLE DEVOURS A CHILD. An authenticated telegram from Wichita, Kansas, says that the baby of William Beattie, a farmer, was carried off by an eagle, killed, and devoured. The baby was a few weeks old, and was sleeping on a blanket outside the house, while the father was at work near by. A little girl ran to him and told him that the baby ” had flied away.” The neighbours were assembled, and the eagle followed to its nest and shot ; but only the skeleton of the child was found.”

Others might be able to find out more about this story- just a tall story, or with some basis in fact?