Assange and a woman have consensual sex. He wants to have sex without a condom, she insist he wears one. Eventually he agrees, and they have sex and then fall asleep in the bed. The next morning she wakes up by him penetrating her. She asks "are you wearing anything?" to which he replies "you". Her main reason she wanted him to wear a condom was fear of STDs, so she thinks there's no point in stopping now since the eventual damage is already done, so they continue. He comes inside her.
When she later asks the police if there's a way of forcing Assange to take an HIV test the police decides that what she's describing constitutes rape, and starts an investigation.
The whole problem is that she gave her consent under the strict condition that he'd wear a condom. When he started having unprotected sex with her while she was sleeping, he didn't have her consent. Call that what you want.
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Edit: OK, I see that that's mentioned later in the article. But the part about rewriting the statement isn't completely truthful either: > "Now the supervisor of the policewoman who had conducted the questioning wrote her an email telling her to rewrite the statement from S. W."
What the mail actually says is that there are two hearings, but only one formal one, and they want the second one included too. The supervisor writes: "Make a new hearing. Paste the text in that and assign the hearing to the case. Sign the hearing."