Oh dear, I hadn't thought of it that way. That makes things so much harder for Zuko, because I think most people fundamentally want to believe other people are like them, that other people are as honorable and loyal and truthful and trustworthy as they are. And it can lead to some Very Bad Things for people who are fundamentally honorable (like Zuko) or trustworthy (like Aang) or truthful (like me - I know I assume strangers are more truthful and trustworthy than I should).
As for Zuko being suspicious... he wasn't until Azula told him she told Ozai that Zuko had killed the Avatar instead of her. He didn't seem to have any problem believing she told Ozai that he had HELPED her take down the Avatar, and he clearly believed her when she said siding with her was enough to get back in Ozai's good graces enough to come home. So... I guess he was suspicious, but perhaps not suspicious enough considering what he already knew.
Re: OP
As for Zuko being suspicious... he wasn't until Azula told him she told Ozai that Zuko had killed the Avatar instead of her. He didn't seem to have any problem believing she told Ozai that he had HELPED her take down the Avatar, and he clearly believed her when she said siding with her was enough to get back in Ozai's good graces enough to come home. So... I guess he was suspicious, but perhaps not suspicious enough considering what he already knew.