When you learn, the concepts shape your thinking. A great memory is required to quote the exact words, but to mention a general location, or a topic without a location, is not the work of memory. When The Frog uses Google to get the words of the Pasuk, obviously awareness of the Pasuk preceded the search. That kind of Bekius in Tanach I am unfortunately far from (as of now).
You might notice that sometimes Sam2 says that he feels like there’s a Gemara someplace. That is because, when you allow the Torah to create your attitudes, instead of twisting it to fit yours, you can eventually assume that the strong bias you have about a certain issue is not unfounded.
Pulling up a Sugya from here or from there is no different than how people pepper a conversation with anecdotes of their life. It doesn’t take a great memory, but it requires active participation.