I've had a few sets burst into flames, but never when unattened. The Zenith Chromacolor II sets were constantly having the high voltage tripler burst into flames, but usually would go out as soon as you shut it off. Also the Sylvania Superset of the early 80s did that. The closest for me to having one go out of control was an RCA KCS-49 21" metal-tube console in a wood cabinet with doors... I plugged it in, and evidently the power transformer was shorted on the primary, which caused the on-off switch to burst into flames. The wires nearby caught fire, and it was VERY hard to put it out because where it was burining was way up in front out of reach. I managed to blow it out just in time! If I had been out of the room, it could have been very bad
I also know of house fires that were started by CTC-16s with faulty on-off switches. There was a bulletin about it in the late 70s. I replaced a few of those, in cases where the switch had caught fire, flames traveled up the wires and set the plastic channel drum on fire.
And one more: The Mitsubishi CK-3502. That set is a menace because when the tuning cap in the standy power supply fails, the 5 volt line goes crazy and burns holes all over the place. There is one board with LEDs on it above the screen, and I've seen that one start flaming through the top of the CRT bezel. I had a customer who had to blow out the flames after they came up through the top!
Charles