The halacha is that generally a keli shelishi does not cause bishul.
The Chazon Ish says that a keli shelishi (or revii) above yad soledes bo does cook those things that are kalei habishul.
A shiur by Rav Yosef Zvi Rimon explains the lenient view
Rashi (Shabbos 39a, s.v. De-sharei) explains that since we are not accustomed to cook in the sun there is no prohibition of bishul in the sun.
For our issue, it may be that the focus of the distinction between keli [sheini] and keli shelishi is the common custom. Most foods we cook in a keli rishon; some foods, such as tea, coffee, baby formula, etc., are commonly cooked in a keli [sheini]; while in a keli shelishi, one is not accustomed to cook at all. Naturally, we may say that even if on a practical level the foods that would cook in a keli [sheini] would also cook in a keli shelishi, there is no prohibition to cook them in a keli shelishi, because this is not derekh bishul, and it does not fall within the boundaries of the melakha.
So here we see that to transgress the issur of bishul on Shabbos, it is critical that the process is derekh bishul even though the food may be cooked in the keli shelishi. (I mean that the constitution of the food may be changed by being immersed in a keli shelishi which can easily be well over yad soledes bo.) Or to put it in other words, bishul is not cooking.
Someone observed cooking going on in a keli shelishi and wants to be extra strict and will not add anything to a keli shelishi which is above yad soledes bo.
How should we view such conduct? Is he inventing his own religion and should be convinced to abandon this view or is there room to look more kindly at his conduct?