... .yet nothing that would amount to anorexia... .it occurs to me how easy it is for such conversations to be invalidating in their own way because when she says something along the lines of "I'm fat" my response of "you're beautiful (or strong, or fit, or thin)" undermines what she sees and thinks.
My ex is anorexic. She has been in treatment on and off over the years and still struggles to maintain a healthy weight. She has relapsed. Until I sat in the therapist's office with her and was told to my face she was anorexic I thought, like you, that her body issues didn't really rise to the level of mental illness. I was wrong.
I have no idea if your loved one has an eating disorder, but please don't make the mistake of armchair diagnosing her; she very well may have something serious going on. I've read about VAT on the website, so I'm guessing that acknowledging her feelings and trying to see if she's open to discussing why she feels the way she does is a step in the right direction? Who knows where it leads? Maybe she wants to know that it's a safe subject and it results in her feeling supported enough to address it head on? Just another Joe Blow with an opinion on the internet, but I've walked in your shoes and it took me really listening and building a foundation of trust with mine for her to take steps toward getting better, and even then it's an on-going journey for her.
Good luck and best wishes.