There is a problem with this suggestion. Why does the Mechaber say that, when Tisha B’Av falls on Shabbos and is pushed off to Sunday, there is a leniency regarding one making a bris milah? In siman 559:9, the Mechaber writes that one who makes a bris milah on a Sunday Tisha B’Av (that really fell on Shabbos) does not have to fast and may wash his body. In contrast, one must fast and may not wash his body if he is making a bris milah on the regularly scheduled day of Tisha B’Av during the week. If we explain that the Mechaber is of the opinion that when Tisha B’Av falls out on Shabbos and is pushed off to Sunday (making Sunday the actual day of the fast, and thus Tisha B’Av didn’t fall in the prior week), permitting one to have marital relations on Shabbos, why is there any leniency or discrepancy regarding the fast on Sunday?
The sefer, Harirai Kedem chelek 2, suggests a different understanding behind the machlokes. He suggests that the machlokes as to whether aveilus betzina applies on Shabbos Tisha B’Av is dependent on a different point. The Rema, who says that it applies on Shabbos, holds that Tisha B’Av is in essence always on the ninth day and therefore aveilus betzina applies. The Mechaber agrees to this, but holds that there can only be one day on which the aveilus of Tisha B’Av can be observed. And since we cannot fully observe the aveilus on Shabbos, we observe it only on Sunday.
Both sides of the machlokes regarding whether there are halachos of shavua she’chal bo the week before Tisha B’Av agree that Tisha B’Av is essentially on Shabbos. However, the opinion that holds that there are no halachos of shavua she’chal bo believes that the halachos applying to the week of Tisha B’Av are connected to the aveilus of Tisha B’Av, not to Tisha B’Av itself. The avelus of the week that Tisha B’Av falls out in is a prelude to the aveilus of Tisha B’Av. So even though the actual day of the fast is primarily on Shabbos, since aveilus is not observed on Shabbos, the week that Shabbos falls out also does not have any halachos of aveilus.