That`s very sad. I can`t honestly offer an explanation really. Everything in her tank sounds fine. I can only think she could have been dropped at some point, or fell when out playing with the owner? Rodents don`t usually get paralysis in the hind legs until they are old, especially rats.
She`s either had some trauma to her spine, or something to have cause degeneration or nerve damage. The squeaking makes me think trauma.
What species of hamster was she?