I have a hard time believing this happened as described: if a woman was out in public in a full burqa, why wasn't she escorted by her husband or father?
This may surprise you, but Muslim women are actually capable of thinking for themselves and making their own decisions.
Under most interpretations of Islamic Law, women are supposed to be escorted by male relatives when they go outside. Numerous Hadith as well as much jurisprudence attest to this. In modern societies, this doesn't tend to be very practical, so it isn't really enforced outside of Saudi Arabia and rural regions of Afghanistan and Pakistan, but these are also the regions where wearing the burqa/niqab is most prevalent, and if a woman adheres to such a strict interpretation of Islamic Law that she feels she must cover her face (which most Muslim women don't do, even in Muslim countries), she should also be escorted by a male relative.
This may make you uncomfortable, but think about it this way: at the end of the day, Islam is really no more patriarchal than the other Abrahamic religions. The difference, of course, is that almost nobody in the West is still trying to follow Christianity or Judaism literally, aside from a few Fundamentalist Christians in the U.S. Heartland and Deep South, and a very small number of Ultra-Orthodox Jews in New York and Israel.
Also, I am not arguing against the agency of Muslim women: far from it, actually. A woman who wears a buraq/niqab may in fact want to be escorted by a male relative both for physical safety and for compliance with the Sharia. Some women actually prefer this. It's just that this type of woman wouldn't be running out of the woods to attack random Georgians with their American flag.