The people doing the interview did say that the show was not going to be back for a second season, and that they were gathering up the final contestants.
I read somewhere that the show was cancelled in mid-season, but Cosby and the producers wanted to finish the season, so that the stations would get their money's worth and that viewers would watch until the end.
Of course, that didn't stop stations from shuttling the show to late-night slots -- I recall a SNL skit from 1993 where a TV station announced they were leaving the air for the night, "right after 'You Bet Your Life' with Bill Cosby!'" Very funny, especially with the guy playing Cosby talking gibberish ("Watch 'The Cosby Mysteries' -- only on NB Flibberflabben!").
Also, Cos's ambition to finish the season didn't stop stations from cancelling the show themselves -- when YBYL statrted in 1992, WFTS ch.28 in Tampa Bay (then with Fox) shown YBYL in the evening (don't know what time exactly -- maybe opposite Wheel or Jeopardy); after it was cancelled, they dropped the show themselves, in which WTMV ch.32 (now WMOR), then a low-rent TV station, picked up the show for the remainder of the season, also in the evenings.
I, myself, enjoyed Cos' YBYL -- especially his quotes that he usually gives at the end of the show.