qa-
If the person is known to keep halacha, then you should definitely assume he has a heter. The gemara’s case is where they saw someone taking off his tefillin, walk into the house of a zonah, walk out and tovel as if he had just done an aveirah, and still they judged him lekaf zechus because they knew he was not the kind of person to do the aveirah. So if you know the person eating the cheeseburger is a shomer torah u’mitzvos you should certainly assume he has a heter – i.e. a medical condition that he has to eat it if he smells it (something the mishnah talks about) etc. etc.
However, if the person is not so careful with halacha there is no reason to be a fool, and I suspect Trying My Best was talking about such people when he/she accused them of not keeping the halacha.