Rihanna.
Beyonce is beautiful, and her fashion choices in recent years have been amazing after some really questionable, cheesy outfits from her Destiny's Child days and early solo career. But that was the 2000s so of course some of her fashion choices were going to be cheesy. And let's not pretend like Rihanna didn't have them too. Her Music of the Sun era outfits were just as tacky.
The thing is though, the term "fashion icon" doesn't imply "looks good at events" and "makes good red carpet choices" - it literally means a fashion icon. Someone who inspires how other women dress, and in Rihanna's case, even how some men dress considering her style can be quite masculine (baggy jeans, timbalands, flannels, basketball jerseys, menswear from runway shows).
Beyonce looks gorgeous at events and her stage costumes work amazingly with her shows, but I mean, Rihanna and her stylist Mel Ottenberg are single-handedly deciding how an entire generation of girls dress. Their decisions are literally becoming generation-defining. Wearing a basketball jersey as a dress and pairing it with Manolo Blahnik sandals? Wearing a really expensive dress and pairing it with Nike sneakers? People will look at that 30 years from now and say "that is so '10s!" They'll have "2010s" themed 21sts and girls will be wearing the styles Rihanna started.
It's Rihanna. End of.
No it means she's NOT a non factor in Fashion, maybe! 
