I believe a kinescope is a crude copy made by pointing a camera at a monitor, or TV during a broadcast, in case the original is lost. Would any station that had rights to the real broadcast show an inferior copy just to have it at a different time?
I never remember the delayed broadcast being in the fuzzy kineoscope version. It was always crystal clear (well, as crystal clear could be back then with rodors and antennaes and scraggliness happening when my mom turned on the vacuum cleaner or the mix-master or a plane flew overhead). I think. Hey! It's not like I'm a nine-year-old anymore! I forget some things.
I also always think of Lara Parker at a 1990s Festival informing fans who asked why Moltke left: "She didn't want to be on the show! She REFUSED to wear make-up!"