This post is a sequel to: Collaboration or acknowledgment?

The following has come to my attention. A senior mathematician (let us call him or her Alice) suggested a problem to a young mathematician (Bobby) who proceeded to solve it on her own and wrote up the result. Bobby agreed (*) to let Alice be listed as a coauthor, but Alice also insisted to include her PhD student (Charlotte) as a coauthor because they were thinking about the same problem, despite the fact that Alice and Charlotte did not even have partial results.

(*) Bobby had no problem with Alice joining her as a coauthor for the reasons mentioned by Igor Rivin below (I include you as a coauthor, you write me a good recommendation). Thus, the credit was unfairly diluted by including Charlotte who had not contributed.

Question: Is there a way for Bobby to manage such a situation without creating conflict?

Full disclosure: I am Bobby's PhD advisor. I can not interfere directly because Alice is a powerful person in the field known for aggressive backing of her PhD students and I do not want to inadvertently hurt Bobby's career.

Update: Following the advice of Joel David Hamkins, Bobby will be the sole author. There is nothing in the paper that Alice and Charlotte could point to as an idea they already had in mind. Looking back, what bothered me the most was not that Bobby's credit would be diluted but that someone who did not deserve it would be rewarded.

I will award bounty points to JDH for his uplifting Thanksgiving Day Answer, but, of course, any new comments are welcome.