I am talking about halachic challah -- the portion taken for the offering. I was taught several times that these days, what to do with it is to burn it to a char in the oven. I also learned that this should be done separately from other foods (source: Halacha section of the Bais Yaakov Cookbook). This is actually a big challenge erev Shabbos, when one is short on time and has a lot of food to cook.
1) Is it true that mitzvah challah must be put in the oven alone?
2) If so, why?
I had thought that the reason for this was that the challah is treyf, but on second thought, that wouldn't make much sense (since we cover it completely anyway; plus, if there were in fact a problem of trefus, cooking it without other foods in the oven wouldn't help much for the kashrus of the kitchen--although there may be some nuance in that matter, possibly related to steam). But a rabbi at my seminary mentioned that it actually may be because we can't derive benefit from the challah, and if we kept it in the oven with other foods, it could be fuel for their cooking.
I understand how that could be true if challah were put in a fire with other foods being cooked above. But how could it possibly be true in an oven? If it couldn't, and that's not true, then what is the explanation for why the challah must be in the oven alone?