I previously touched on the difference between a chovas hatzibbur vs. a chiyuv on the yachid to fulfill in a tzibur with respect to megillah; the same applies to keriyas hatorah, as Chaim Markowitz discusses here: http://nefeshchaim.blogspot.com/2006/02/parsha-chabura-beshalachthe-obligation.html According the the Ramban in Milchamos (page 3 in dapei hari"f) in Megillah, it sounds like keriyas haTorah is a chiyuv that applies only to the tzibbur, not each individual yachid. In R' Rakkefet's book about the Rav, this issue is mentioned in passing with regard to R' Soloveitchik's commute from Boston to NY, which sometimes entailed missing tefillah b'tzibbur and keriyas haTorah - if I recall correctly from the book, the Rav's practice was to take out a sefer and lein, despite the fact that he was only a yachid who was mechuyav and the tzibur was already yotzei. This despite the fact that the idea of kr"ht being a chovas hatzibur is often quoted in the name of R' Chaim. I am not sure why the Rav was unconvinced.
Despite mentioning this lomdus by megillah, I did not realize the implication with respect to the common practice of leining zachor a second time for women after the regular davening. I have always had a pet peeve with these leinings because there are usually done without a bracha. According to R' Chaim (quoted in GRI"Z al haRambam, see also Emek Bracha) birchas haTorah is on the cheftza shel Torah, not the chovas hagavra. Even if you are leining for women who have no chiyuv, you should say a bracha because you are engaged in reading a text of Torah, irrespective of the chovas hagavra.
However, I missed the real issue here. Yesterday the minyan did not do a second leining for the ladies who missed the first. R' Z. Friedman explained that if keriyas haTorah is a chovas hatzibur, then unless there is a tzibur of people who did not hear leining, one cannot just take out a Torah and lein for a yachid - that is not called keriyas haTorah! Of course, those who were affected by this issue simply walked to a neighboring shule where I guess they are less convinced of Brisker lomdus and do do a second leining, but unless you reject the Ramban, it would seem this chiddush is correct.