It sounds more like an issue of self consciousness to M..
I am not sure what you are talking about.... the "headlights" showing when she is chilly or the nipple itself?
In any case, it is a normal part of the body. I am a 34DD. I do not like liners, padding, seams, etc on my bra. I like a smooth look that is natural.
My suggestion is to go to someplace like Nordstrom or Neimans and get professionally fitted. Find a style she likes that she is more comfortable wearing. Personally, I would never wear a white bra. All of mine are nude/flesh toned or black.
It looks silly to see band-aids through a grown woman's shirt. The band-aids are more noticeable than the nipple itself! It screams low self esteem.
I know with the way I like to wear my clothing, I do not wear white or very light colored shirts you can see through. I can wear my favorite bras and still look nice wearing the same shirt but in a darker color or pattern.
Best wishes.