Jane: “I never said he licked my asshole.” <-- He never licked my asshole, and I never claimed that he did. Adam is lying about both parts.
Jane: “I never said he licked my asshole.” <-- He licked my asshole, but I never told anyone that he did. Adam learned about the asshole-licking from someone other than me.
Some context might provide the distinction.
Adam: “Jane told me that he licked her asshole.”
Also “I never said he licked my asshole” can mean I implied it heavily.