The general rule regarding telling someone to do something you do not hold of, is that it depends on whether you hold that it is strictly forbidden, or merely a proper Chumra with room to be lenient. In the former case, one cannot tell someone to do something for him (i.e. push a stroller for him in a place where there is an Eiruv the other person uses, but he himself holds is not an Eiruv at all), and in the latter he can (i.e. the above case where he does not carry but holds that there is room to say one can use the Eiruv). The same goes for different Hechsherim. If one would hold the food is Treif, he cannot give it to someone, whether or not it has a Hechsher. If he merely does not rely on the Hechsher but holds that there is room (using Rovs, Chazakos, Heteirim etc.) to use the Hechsher, he may pass the food. Being that this is the case, I don't think the first explanation is correct, as it would seem clear that the Shamash would not hold the food is actually Treif if Rebbi Chanina held it was Mehadrin. It could be that a combination of your possible explanations is correct: that Rebbi Chanina did not want to ask his Shamash to serve him something that the Shamash was stringent in not eating, as it is simply not great manners to ask someone who holds a certain food is Assur to serve it to you (i.e. asking someone who doesn't eat Gebrokst on Pesach to serve you some real Kneidlach).

The Tzitz Eliezer (12:53) quotes sources indicating that Rebbi Chanina was telling the Shamash that he should cut off the *cooked* fat from the *cooked* meat, and *the Shamash* could proceed to eat the meat. These sources basically maintain that although the Shamash held it was forbidden, since it is closer to being permitted than forbidden (meaning that it is a big Chumra), he did not have to be Makpid on the fact that the meat was Bolei'ah from the fat. However, there are clearly those who would argue with this explanation (see Tzitz Eliezer, ibid.).

Kol Tuv,

Yaakov Montrose