I noticed this twice in the last couple of days while doing the Pentagon missions for the manhunt.
Each time, I fast traveled to the Pentagon Safehouse (as opposed to going directly into the missions), and pressed X to skip the cutscene that always plays while loading. The game loaded me into the safehouse before all the dialog from the cutscene could finish, and whatever line of dialog was on the screen at the moment I loaded in, wound up staying visible on my screen, permanently.
Logging out doesn't even fix it, I have to quit out of the game entirely and then load it back up again to get the text to go away.