You are correct about the genetics,they are sisters!
I just wanted to set my mind at ease that it wasn't anything I was responsible for!
I think from the general jist of comments I'm not and there's not a lot I can do!
I'm certainly no expert in PS and think I would make things worse,trying to fix it,if it can be fixed.
It's probably more noticeable to her than anyone viewing the images,especially at normal sizes and viewing distances!
Its still a tricky one, and a lot depends on what the bridesmaid "actually" said, and the tone it was said in. Is she angry at the "incompetent" photographer, or is she aware of her appearance, a bit disappointed it's so obvious in some of the photographs, and wondering if it can be improved a little with a bit of retouching. And if the latter, maybe say that "retouchers" and "photographers' are two different professions and to make a good "natural" looking fix would require (her) paying for a retoucher. Assuming you don't want to have a go yourself.
For me, the first action would be to go back to the groom (and maybe the bride), and discuss this a bit further. And maybe from them, see how sensitive the bridesmaid is about it, and then try to talk to her directly.
I would be approaching this with a mix of facts (I do seems to have caught you at unfortunate moment, but that is how you must have looked at the time. It isn't possible to look at everyone in the picture and I was naturally focussing on pressing the shutter when the Bride and Groom looked good), coupled with empathy on how to deal with it. Is it that she doesn't want photos of her looking like this in her sisters album, if so then agree with the sister not to use the worst ones. Maybe agree (with the bride and groom), to crop her out of a picture, if its one where the bride and groom are particularly good, and she is particularly bad, as long as there are plenty of alternatives where she can be in a picture.
If she wants a 201 x 16 of a particular image for her wall, where here eyes are especially bad, then look at then look at building in the costs of some professional retouching into the print cost.
I'm obviously just thinking out loud here, but these are approaches I would be approaching, and I would certainly be trying to find out more details of her "exact" concerns, especially now that you feel confident you aren't to blame.
Cheers,
Graham