I think you've zeroed in on why I'm so stuck on the opposite side of the argument. To me, it's absurd that an attack could "score a critical hit" and also not hit - precisely because the word "hit" is used as it is. If the authors intended for a 19 not to constitute a hit, it could have been phrased to reflect that: "If you roll a 19 on a weapon attack and hit, your attack is a critical hit," or "roll damage as if you had scored a critical hit."
Another issue is that Improved Critical's language includes both to 19s and 20s. While this is largely a RAW discussion, it's worth dipping into RAI a bit here: if the authors intended for one rule (critical maybe-hit) to apply to 19s, while the normal rule (critical always-hit) applies to 20s, why would this class feature be phrased as though the same rule applies to both? It seems that by including "or 20," the text is communicating that the purpose of the class feature is for 19s and 20s to function identically for the Champion.
Both sides make so much sense...