The gemara seems to imply that in a city where the custom is to give the gabai tzedaka who will then distribute to the poor, one would not have an obligation to give to a poor person who knocks on the door. It is interesting to note that the chofetz chaim in his sefer Ahavas Chesed (2:17) has an elaborate footnote screaming about the terrible system of collecting all money in some sort of keren and not allowing the poor to collect individually in the city. How does that fit with the system that the gemara assumes to be the norm? Perhaps the system that the gemara refers to will still allow the poor to try and collect, but one is not obligated to give since he has already contributed to the keren, whereas the chofetz chaim was speaking of a system where they would not allow the aniyim to collect at all (but it doesn't sound like that from what he says).
A second point is: R' Asher Weiss (Breishis 38) discusses one's obligation to give all their possessions to an ani collecting for a situation of pikuach nefesh. He concludes that one is definitely obligated to give ALL their assets as the chofetz chaim writes, but: סוף דבר נראה ברור לענ"ד דחייב אדם להוציא כל ממונו להציל נפש אחת מישראל, אמנם זה רק במקרה קיצוני שהוא לבדו יכול לעזור. אבל ברור ופשוט שאין האדם חייב למכור ביתו וכל אשר לו להציל חולה וכדומה כשיש רבים המצוים להציל ומהיכא תיתי יתחייב הוא ולא אחרים שמצוות התורה מוטלת גם עליהם, וזה ברור ופשוט
R' Asher ends up saying on his own the concept that we find in our gemara: "not every person who becomes poor falls on me to support" - meaning that one's responsibility is ultimately to contribute their share along with everyone else. BUT, it is a big chiddush to apply this concept in a case of pikuach nefesh.