TheBigOne: You are wrong in your definition of Chillul Hashem. The reason doing an Issur in public is Mechallel Shem Shamayim is because it gives an improper indication of what Hashem wants. Hashem wants us to follow Halachah. By publicly flouting Halachah, one (seemingly) shows that Hashem considers such a behavior acceptable. As such, someone improperly represents Hashem.
No one (well, very few people) are claiming to represent Hashem’s will when they publicly admit to doing Mishkav Zachor. As such, Shem Shamayim is not Mechulal because no one is claiming to represent Shamayim in this process. It’s no Chillul Hashem if someone who knows nothing of Yiddishkeit (or a Goy) does something Assur in public. That’s not the point.