The 39th People's Choice Awards ceremony, honoring the best in popular culture for 2012, was held January 9, 2013 at the Nokia Theatre in Los Angeles, and was broadcast live on CBS and simulcast over Xbox Live at 9:00 pm EST. The ceremony was hosted by Kaley Cuoco. The nominees were announced in November, 2012.
The 41st People's Choice Awards were broadcast live on CBS
The context states that the 39th People's Choice Awards were broadcast live on CBS, but does not give any information about whether that happens every year or not. There is no way to know based off the context alone if the 41st ceremony was broadcast on CBS. The system was likely confused because the statement uses a different number for the ceremony than the context.