That’s all very interesting, but the actual question was related to the fact that when the aeroplane sees a temperature of above 10C, the EAI selector is ON and there is no ice detected, it will bring up a checklist asking for you to turn it to AUTO or OFF. Should you ignore this checklist?
My answer is that unless you feel the measurement is significantly in error (and that’s going to cause other problems), then it is SOP to action the checklist in the way that the manufacturer intended, otherwise they would not have made it pop up in the first place. If you choose to ignore the [ ] ANTI-ICE ON when it appears, what new threshold are you going to use to determine whether it should be on or not, as you’re going to need one if you don’t trust the aeroplane?