According to Cooper by Woolfenden & Elkinton, pp. 24-31:
California's new governor, Luis Argüello, purchased Juan Bautista Rogers Cooper's ship Rover in December 1823. The vessel was loaded with seal pelts and sent to Canton, first making stops in Honolulu, Fanning Island, and Manila. It reached Canton in June 1824, returning to Bodega Bay by October 23, 1824. In January 1825 it picked up more peltry in Monterey and headed to Canton again, returning the following year. Most pertinently, prior to its return,
There was a rumor current, circulated by a certain Captain Newell, that Cooper's co-owners had failed in business and that he had run off with their ship.
(According to Don Francisco de Paula Marin by Gast & Conrad, George Newell was master of the Mentor, which arrived in Honolulu December 1, 1824.)
Kotzebue left San Francisco on November 25th, 1824 (possibly old style). His book does not refer to the Rover, and Cooper's biography does not mention Kotzebue. Insofar as Cooper's long journey was just ending, and the two captains did not cross paths, Kotzebue seems to have taken the rumor of Cooper's disappearance as fact.