Wow! Getting fired for sending inappropriate e-mail at work is nothing new, but how about for just receiving it? This really does smack of a vendetta; after all, it doesn't take a technically-savvy supervisor to ask the employee who complained for a forwarded copy of the offending e-mail message. Yes, said supervisor might be fooled by a forged message, but I'm guessing this hospital employee wouldn't be capable of that. And if they fired her for showing a printed copy of the e-mail message, they should've asked for a witness to corroborate the story.
That aside, if a complaint were filed against me, I'd hope they'd go to the mail server log files before canning me! She was her family's sole provider, for crying out loud!