Possible bad batch of Toyota fan clutches!


So I recently started experiencing higher than usual temperatures. I had just had my timing belt service completed which included replacing all the coolant, water pump, and thermostat. I had the dealer replace the fan clutch. The next day I had the same issue with higher temperatures. My scan gauge showed 249 degrees and the dummy temp gauge on the dash was just about to hit red when I shut it down.
So with the engine shut down at 249 degrees the fan continued to spin for about 5 more seconds. Pretty obvious the new clutch was not engaged right?
I brought it back to the dealer and told them it was bad. They replaced it again today. I immediately drove around for an hour and experienced the same higher temperatures. I parked in my driveway and let it cool down for about an hour.
At 150 degrees I took a rolled up piece of paper and pushed it into the fan and the fan kept running strong. I shut the engine off and there was resistance in the clutch.
I then drove around the block and brought the temp up to 182 and when I pushed the rolled up paper into the fan it immediately stopped and had no resistance.

Am I misunderstanding how these fan clutches work or do I have the worst luck in the world to have my original fail as well as two brand new ones?