It's worth noting that technically 20 is only an auto-success on attacks and saves. The way you describe is a very common house rule, but it seems to frequently be an accidental house rule (more of a misreading).
Has it changed over time? It looks like what you say is true in 5E, though only for death savings throws. But I played 3.5E. My memory isn't good enough to know whether that makes a difference.
I looked it up in the various books I have on my shelf:
D&D Redbox:
No skill checks, Attacks succeed if the modified value is 20 or higher. So a level 1 Str 9 character can never hit AC -1. A level 1 Str 18 character needs only a 17 to hit any AC. These rules are different in later rulebooks when the THAC0 is introduced.
[edit] Checked my Expert rulebook, and found that the modified 20 always hits is just due to very low ACs not being represented in the Basic charts (In OD&D lower AC is harder to hit). The target number to hit goes up as AC goes down, but "sticks" at 20 for 5 points of AC. There is no special rule for auto hitting or missing with a natural 20 in OD&D. Note that monsters are quite good at hitting with the weakest monsters hitting about as well as a mid-level fighter with mundane equipment.
D&D 3E: Only attacks succeed/fail on a natural 20/1.
D&D 3.5E and Pathfinder: Attacks and saves succeed on natural 20/1
Too late to edit, but thiefs do have skills, and these are d% and always fail on a 100, which is a 1% failure no matter how good. Also, I forgot how bad pickpocketing is; if the opponent has HD equal to your level you have less than a 20% chance of success throughout the intermediate levels.
