I think the way it went down is that the pit bull told someone else (another friend or neighbor?) that she had overheard the conversation and that Burke was talking nonchalantly about the manner of the strangulation. The person she told about it then told BPD. When they asked Stine about it, she denied it.
***ETA: Found the reference in
FF. [Mary Ann Kaempfer had a son (Anthony Pecchio) who was a classmate and friend of Burke's]:
While attending the memorial services in Boulder, and while playing with Anthony in Atlanta, Burke was described by Anthony as acting like he kind of knew what happened and trusted that
people would find out.
Anthony indicated that Burke may have appeared confused at times, but was not acting upset and indicated that he was not scared. When asked how he was doing, Burke said he was fine. Anthony told investigators that he never saw Burke cry during their stay in Atlanta.
Kaempfer advised that the only time she had seen him display some emotion and sadness was at the cemetery after the graveside services. He had left a group of people and went to the side of JonBenéts casket, patting it gently.
After that brief display of caring, Burke and Anthony went exploring, skipping through the headstones in the cemetery.
Upon returning from Atlanta on January 2, 1997, Kaempfer spoke to fellow parent Susan Stine and was told about a conversation Stine had overheard taking place between Burke and her son, Doug. This was reported to have taken place on the afternoon following the grief counseling session that had been hosted at JonBenéts school on the morning of Saturday, December 28, 1996.
Stine appeared to Kaempfer to have been disturbed by the conversation and had listened to Burke and Doug talk about how JonBenét had been strangled. Based upon Kaempfers statement, it appeared that Stine had over overheard the boys discussing whether or not manual strangulation had been involved in JonBenéts death.
Stine described the conversation as being very impersonal, and it struck her that the discussion about the details of JonBenéts death was like the boys were talking about a TV show. This discourse between Burke and Doug had taken place no more than 2 days following JonBenéts murder and apparently had such an impact upon Stine that she brought it up in conversation with
Mary Kaempfer at the first opportunity.