I believe GameCube games aren't supposed to be precisely 4:3 or 16:9 due to their funky pixel aspect and variable storage aspect. So it's normal to have a small amount of black bars at the sides or top and bottom, depending on the game.
All that matters is whether shapes that are supposed to be symmetrical appear symmetrical.
Nintendont seems to be handling this correctly when set to auto width, according to ruler measurements I've taken from NTSC versions of Mario Sunshine, Twilight Princess, Wind Waker, and Skies of Arcadia.
If you don't set Nintendont to auto width, I believe you will end up with some games displaying incorrectly, as I've observed the auto setting does in fact adjust the width on a per-game basis. The best example of this is Twilight Princess, which renders internally 666px wide, and only displays symmetrical squares on its test pattern when nintendont width is auto or 666.
Please let me know which game doesn't look right with auto width, as I would like to investigate.