Just as a sidenote, it does matter for the FICO score, at least according to equifax. I got an online credit-report from them, and they let you experiment with your info to see how it affects the score. By removing my CC balance, I went from 714 to 724 on their FICO score.

Of course, whether Equifax's FICO score is an accurate indicator of credit approval is quite another matter, as you are saying.