I think you're misinterpreting what a successful decieve roll actually means as it applies to a player. All it means is that the player, and thus the character, thinks the NPC is telling the truth. There's absolutely nothing that compels the player to believe that the statement is true or especially to act on it. The roll doesn't determine what the player or PC believes though. The player can decide to act on that information however they like. Roleplaying doesn't compel the player to act either, althought they could. I know this is similar to what you're saying, but I don't think that the phrase "do what the character would do" is especially useful here except as a very loose rubric.
Personally, just because an NPC makes a skill check I'm not likely to do somethign with my character that I think is stupid, and I wouldn't expect anyone else to. As a GM I never roll skills like this against PCs for this reason - I leave the reasoning bit to the player. I'll give them the info and they can roll to see if they detect falsehood if the system has such a mechanic. That's more than enough IMO. I think it's illustrative that many RPGs don't have anything like that mechanic and still manage to social interaction just fine.