IMHO, a CarFax claim for $800 probably won't affect the value too much. But what kck6894 said is probably the best idea. Just pay for it out of pocket. What's the deductible on your friend's insurance? Is she really going to save money in the long run by filing the claim or would it be cheaper for her to pay cash to get it fixed?
As to the diminished value route, I doubt normal insurance will allow for that. I think that's only in collector/specialty vehicle policies. Is that what you have on your Mustang? If so, then file that claim against your own insurance policy.