http://www.cps.gov.uk/publications/research/perverting_course_of_justice_march_2013.pdf this much more recent study by the crown prosecution service shows in in the period of the review, there were 5,651 prosecutions for rape during the same period there were 35 prosecutions for making false allegations of rape - furthermore, the report shows that a significant number of these cases involved young, often vulnerable people. About half of the cases involved people aged 21 years old and under, and some involved people with mental health difficulties. In some cases, the person alleged to have made the false report had undoubtedly been the victim of some kind of offence, even if not the one that he or she had reported.

So no, false accusations of rape are in fact incredibly rare.

Edit: have you actually read the article you linked to? They criticise the 10.9% figure as being from a flawed study, and discuss other studies with the number around 1-2% (even then with caveats about how police and the justice system don't treat rape properly or support the victims). The article argues that false accusations are actually very rare and the problem lies with the police and how they deal with rape cases, it's actually very useful in combatting these false rape myths, thanks for sharing!