There is flawed logic and there is just lack of knowledge or just plain ignorance. I believe you fall in the former two categories.
No oncology expert would ever say that radiation treatment machines are safe. They are not. They (should) deliver just the right amount of radiation to kill the cancer and not healthy organs. You are making an argument about a topic, which is completely unrelated. Radiation machines are gamma rays, this is infrared. The logic "radiation is radiation" is simply flawed.
Again, we are talking about radiation levels so low (think about it... it runs from a small battery) that it represents a negligible amount of IR radiation absorbed during the day. I would argue that cooking breakfast on a stove (not induction) gives you a thousand times larger dose.