I always have the impression that "they didn't admit to a crime" tends towards implying that "they" are guilty, while the wording "they denied committing the crime" doesn't have any such bias. Is this just me or is there evidence that lots of people see it like that?
Headline: "Adam Smith denies sexually assaulting Eve Miller" Subhead: "Prominent critic Sally Johnson demands him to withdraw his bid for presidency, but he refuses to do so because of unsubstantiated allegations."
Headline: "Eve Miller: Adam Smith molested me!" Subhead: "Critics have demanded him to withdraw his bid for presidency. Adam Smith did not admit to the crime."
Both of those are subtly (or less subtly) biased no matter whether the intuition described in the first paragraph is true, but more so if it is.
Maybe it's because not admitting doesn't imply denial (but the accusation stands, so there is only one opinion) and denying the crime explicitly creates two opposing opinions regarding the guilt of the accused, but I can't quite put my finger on it.