The study in question is from Oxford University and claims equal rates. Indeed, it may be wrong. However that's kind of the point - this thread is full of people making claims about vaccine efficacy or safety, but for basically any claim you want you can just plug it into Bing or DuckDuckGo and immediately find scientific studies that appear to contradict it. Science can tell you almost anything and everything, it seems, so no big surprise that people find it hard to trust.