"There was a lack of detail," sheriff's Capt. John Thornburg said at the time. "The son, who reported it, couldn't even tell us where he went in under the water."
Gordon's son was returned to Scotland with the help of Monterey County Child Protective Services. He did not face charges for filing a false report.
Gordon, who is from the Edinburgh area, is wanted on 24 counts of rape in Scotland.
"When that came up, we start to wonder if this is a hoax, and he's trying to escape these charges out of Scotland," Thornburg said.
A spokesperson for Police Scotland told the BBC: "Police Scotland is aware of reports from the USA regarding Kim Gordon or Avis and is liaising with the relevant authorities."
- AP