I'm not quite sure I understand the question. "Who do you trust to handle the major issues" and "which party do you identify with" are not the same question, if that's what you mean. They don't get at exactly the same thing, and it's even harder to say "independent" to the "who do you trust" question.

If you're asking why do Democrats usually win on that question, with the implication that it's not plausible they always win and results must be biased, well, up until 2000 Dems had a substantial lead in party identification, so it's not all that surprising. Even in the 2004 election, polls showed Kerry generally winning on questions phrased like that, just as Gore beat Bush on most "handle the issue" questions. Bush beat the Dems on polls specifically national security, values, likability, etc. But "best able to handle issues" isn't the same as, "who would you vote for". Dems in generally tend to do better on questions phrased like "best able to handle issues" then they do in actual voting.

Party ID trends: