(like the ability to see the positive side of awful situations) without some of the negative ones (like the obsessive apologizing for everything!)

Since I used to have both of those, to some degree, I don't think they're exclusively Japanese (though maybe more common?). I think, though, that they were the two sides of the same coin-- "Please, please, find me worthwhile and not hateful! Look, I'll like you very much, even if you're rude to me, and see good sides of you-- so please don't dislike me?" I think one can keep the ability to see the good in people once one has it, even after one loses the underlying insecurity-- but it definitely starts out a mix.

(I used to totally, totally, immensely identify with Tohru. Now... well, I want to see what she's like when she grows up.)