I don't think the public loves her. I don't really think most of the public even thinks of her. I think she's maintained a moderate to solid relationship with the media and the mainstream because she's never been a big enough presence to create enemies. Beyonce was making New York Times-caliber news just from her vacation in Cuba. Rihanna posts pictures of herself smoking weed on Instagram and nobody seems to bat a lash, meanwhile they roast Miley on a spit for smoking one at a concert. Aside from the Chris Brown-related stories, Rihanna isn't really on the radar of the BIG media outlets, like The New York Times, late night talk shows, news shows, things like that. She's very prevalent in the pop music scene, yes, but that doesn't mean that she's spoken of outside of that context. I think there's a separation in people's minds between being successful on radio or iTunes, and being a major pop cultural force. Is she a very famous woman? Of course she is, and I'm not doubting that. But given her success in the pop music sector, her brand power is actually relatively small. It seems to me that it's mostly just pop music fans that are overstating her brand power or pop cultural relevance, and aren't willing to remove themselves from that context to look at her across the broader spectrum.
I don't mean to make this another "I'm shitting on Rihanna" thing though; I think she does have the potential to get her brand up there with some of the bigger girls, but it seems to me that she's doing it quite gradually.