I do realize that KPTK isn't the only CBS/StreamTheWorld station to be affected by this "segmentation" problem. When I've heard the online stream of WRBQ/Tampa Bay, going into a stopset, I would hear about a minute of a song played on the air about ten minutes prior, then the online spots would begin.
At any rate, I did notice that, as of yesterday morning, the problem appears to be rectified with respect to the KPTK stream. It proves that they really do care about their listeners - be it in Seattle or elsewhere...