There are exceptional people around, and I don't know your situation, but unless you have already lived in Japan long term, or properly learned the sounds at a very young age, I doubt your accent/speech is indisguishable from a native speaker's.
I never said it was indistinguishable from native speakers, I said it sounded more natural... And I don't think this is something that requires an especial talent... There are gaijin TV personality that have quite plain intonation...
As you pointed out yourself, it seems to you that its very difficult for Japanese to lose their accents when speaking English. That's because you as a native speaker can hear the accent in even fluent Japanese speakers of English. I suspect Japanese can do the same with you in reverse and are just, as always, slightly exaggerating a compliment for your benefit.
I really don't think this is correct, from speaking to linguistics majors and the like... the languages ARE different, and learning them from different aspects and groups of people will of course be different... I never said anything to make myself sound better than my Japanese contemporaries... and they would know this here. If you don't think there are fundamental differences in the primary linguistic structure of Japanese and English, I think you are missing the point.
People who grew up with Japanese in the household, despite not studying it at a young age, or lived in Japan 5 years+ in a full immersion environment might lose the accent entirely. With that said, I've met plenty of people who have studied the language for a long time, lived here long term, and still have accented Japanese (despite relative fluency). Nothing wrong with that I say.
I think these assumptions are specious reasoning... I know people too... most of those who speak with a slightly less pronounced accent are second-generation... but I'm not basing my judgment on that. I'm basing it on the constructs and sometimes seemingly arbitrary rules for pronunciation of the English language...
Japanese is spoken with very little mouth movement, and English the opposite... You'll see this on television when the Japanese are making light of English...
I find it slightly insulting that you think that I'm trying to impress anyone by my usage of the language... I'm the first to admit that my language skills fall far lower than my usage of the language in speech... But, allow me this one attribute.
I think the problem is that many English speakers feel that they are aping Japanese culture, by sounding TOO Japanese... I just don't believe in that logic...
However, pronunciation or no, a firm understanding of grammar and vocabulary trumps pronunciation, and I admit this.
ps. I've heard English spoken Japanese that sounds like it's being read from a textbook, and English spoken Japanese that sounds closer to what you hear in Japan... again, I don't think this is something extraordinary.