R. Shesheth used to turn his face to another side and study. He said: We [are busy] with ours, and they [are busy] with theirs.There is a (seeming) contradiction with a gemara in Sota requiring silence, even in devar Torah, while the sefer Torah is open. And while some Rishonim and Acharonim find a resolution, the general approach seems to be to limit this practice to extremely limit, if not nil, circumstances. (However, there are those Rishonim and Acharonim who do provide a path.)
However, my read of the gemara is that this is not the case of leniency, and thus of discussing a matir. Rather, Rav Sheshet was promoting a lechatchila, and something that someone should be doing, optimally. This time in shul is for learning Torah, and those who can more profitably engage in more advanced study should do so.
I don't know that this means Daf Yomi and those who learn it, and that people would not otherwise have benefited from simply listening to the leining.
Here is what the Rosh has to say about this gemara:
Rav Sheshet would turn his face and learn. He said, "We with ours and they with theirs."
And if you say, behold we say in Sotah, inperek Eilu Neemarin (daf 39a): Once the sefer Torah is opened, it is forbidden to speak, even in a matter of halacha, for it is stated [Nechemiah 8:5]
ה וַיִּפְתַּח עֶזְרָא הַסֵּפֶר לְעֵינֵי כָל-הָעָם, כִּי-מֵעַל כָּל-הָעָם הָיָה; וּכְפִתְחוֹ, עָמְדוּ כָל-הָעָם. 5 And Ezra opened the book in the sight of all the people--for he was above all the people--and when he opened it, all the people stood up.
And one should not say that here is different, since he turned away his face, for if so, it should have included the case of Rav Sheshet there [in Sota] so teach us that in such an instance, it is permitted.
And it appears to me to explain this that it is stated there [in Sotah] "it is forbidden to speak] is specifically in a loud voice, since it prevents others from hearing, but silently, it is fine.
And this that he turned away his face, the same would be if he did not turn away his face, so long as he was able to learn silently, but it is teaching us something extra, that even where he turns away his face, such that it looks like he is putting away the sefer Torah, it is permitted. And he turned away his face in order to focus his attention more to his learning.
Rav Alfes [=the Rif] explained that it was specifically Rav Sheshet, whose Torah was his profession.
But to teach [out loud] to another person, who asks at the time, or to explain something, it is forbidden. (Other sefarim have it: [to explain] issur veheter, no.)