TM exam question: the right of publicity v. comparative advertising

What if Coco Chanel had been the plaintiff in Smith v. Chanel?  This question made me very happy, and I got a bunch of interesting answers on my final:

Kim Kardashian is famous for being famous. She is a highly successful influencer whose Instagram endorsements cost hundreds of thousands of dollars. She has lent her name to a perfume, KARDASHIAN BY KIM. Beautified also sells perfume. Beautified begins an ad campaign that states, “If you like Kardashian by Kim, you’ll love Beautified, with the same yummy smell but a lower price!” Assume there are no choice of law or other procedural issues. Explain why Beautified is or is not liable on Kardashian’s right of publicity claim under California law.