If you really, really like your job, I think it depends on who has more power over hiring decisions -- your immediate boss, or the higher ups. If you already have the full time job, then it's easy to just "go with what's right." But I think you have to look after yourself first... Depending on the situation, if you think she is going to be gone no matter how many supporting statements she gets, then it might not be in your best job interest to side with her. But if the claims are indeed silly, she has direct hiring powers, and it's likely that she's set to stay, then supporting her could help you get that full time position...
But if you don't like your job and can easily get another one, you probably would sleep better going with the truth.