I just want to say that, regardless of how the term has sometimes been used, giving the benefit of the doubt is not the same thing as thinking the best of a person/situation.
Giving the benefit of the doubt means that, if there is doubt, then one ought to hesitate to assume the worst. Basically, if there are two equally plausible explanations for something, and one of them is a nicer spin on the situation than the other, it is giving the benefit of the doubt to go ahead and assume it's the nicer spin.
So in the burger situation: without a whole lot of background information, I think it is plausible that the person who touched the burger that wasn't hers did so with the full knowledge that it couldn't possibly be her order. It is at least equally likely that she touched the burger because she thought it was hers, and only realized her mistake after the fact.
So in that situation, giving her the benefit of the doubt would mean assuming she didn't mean to touch a burger that wasn't hers, and dealing with the situation as though her actions were unintentional. That type of judgment about the situation is far more likely to lead to ongoing polite behavior, and in general, is a much healthier way to live one's life.
That's not the same thing as the cutting in front for the bathroom incident in the special snowflake thread. In that case, even giving the person who cut the benefit of the doubt (that they needed the bathroom urgently), their behavior was still rude.
And a third type of situation would be, for instance, someone glaring at you when you pass them on the street. It is theoretically possible that there was some benign reason for their glare, but it's a whole lot more likely that they were just being rude. In such a situation, there is no doubt to give the benefit of.
Giving someone the benefit of the doubt really shouldn't require any mental gymnastics at all. It should be when you are confronted with a situation that has more than one plausible, readily apparent explanation. Going around assuming the worst of those is really not polite at all, and can certainly lead to behavior that, while perhaps not rude, is more confrontational than necessary.
A lot of the utility and point of etiquette is to, in general, raise the level of interaction in society. That's one reason why you do not respond to rudeness with more rudeness -- in so doing, you decrease the overall level of civility. Part of the goal is to keep the level of civility as high as is possible, which is the biggest reason why it is good etiquette to give the benefit of the doubt whenever possible.