In our shul there is a small group of daf yomi learners, who learn by themselves (myself included). We often discuss the daf or include references to it in our conversation.
I generally do the daf during davening, not during the actual prayers, but during Torah reading, or when the shatz repeats shemona esrei. Sometimes, I'll see something in Rashi or something that doesn't make sense in the daf and I want to go and show it to someone. Then I remember. I am not Jack. And I hold myself back and wait until after davening till I discuss the daf.
There was this baalabus in a yeshiva (somewhere in America) that spent the entire time on shabbos davening learning. I never saw him with a siddur in his hand. We'll call him Jack. Probably a couple dozen times during the davening he would yell loudly to the mashgiach, "Look at this!!" As if the mashgiach had never seen whatever it was that he was looking at. First of all, we didn't like Jack, or his kids. Secondly we felt that it was the wrong time to be having a chavrussa.
Now that I'm more grown up, I realize that davening is an excellent time for learning. I understand that it is the wrong time, as I should be concentrating on the prayers, and when I have my boys with me I don't look in my gemara at all (Educational purposes). But it is a time when I have dedicated to religious time, so instead of reading the Torah pamphlets that everyone else is reading, I go through the daf.
But I am not Jack. I don't disturb other people's davening with my insights or questions on the page. I am not Jack, I spend time actually davening during the service. I won;t say that I am doing it correctly, but at least, I am not like Jack.