I had "Background chat" setting set to off from 1.03 to 1.04 and never had an issue with them. Just updated the game to 1.05 and even though the setting is set to "disabled" in the Interface section these annoying subtitles over NPC heads are on.

Am I the only one with this issue? Are CDPR developers so inept that by fixing one bug they introduce 3 new ones?

Ignore what I wrote about background chatter. There is a separate toggle in the Sound menu, under Subtitles, called "Overhead". I'm not sure if it was there all along and 1.05 just enabled it for me for some reason but why have two of them? Who knows.