Did you work on Betty GBA at all?

Nope.  I did all the art for the Three Stooges cell phone game though.  It's not amazing, but we crammed a lot in for a cell phone game, heh.

Tsu, you say 'what if the character walks over a pure white wall'. This doesn't happen.

Black ninja character.  Night-time background.  Gone.  White ninja character.  Looks great in every level except the snow level.  Gone.  A single sprite, or pic, on a single background or two is fine, you can plan around it...but when you have a full project where you've got say, 6 or 7 different background titlesets (forest level (greens), water level (blues), snow level (whites), lava level (reds/yellows), etc.), and you've got more than one character, and you've got another artist working on backgrounds at the same time you're working on characters (so you can't even guess what the lava level will look like, let alone adjust your colors for it, until it's made...same thing with the background artist not being able to adjust his tile colors to your characters you haven't done yet), selout will save your ass.  In an ideal world, you can take a month and adjust the colors of every single sprite/tile to every single tile/sprite, but working on an actual project, it's inefficient.  In a world with firey backgrounds, your fire spell will vanish.  If you can just cut out the fire level entirely, great, but generally you can't.  If you can just cut out the fire spell, great, but generally you can't.

Sprites always have more saturation than backgrounds

Generally true, but remember the platform you're viewing on.  It's not always going to be a nice pretty super-bright/intense PC screen where you make your sprites.  The GBA screen dulls all of your colors (a screen that's "pure white" will look greyish-blue to the eye).  There almost ISN'T "saturation" on that damn thing, heh.  The DS is much better, but it still messes with the intensity and colors get tinted to blue.  Subtleties that show up on a PC screen don't translate over.  Selout works around that.

You can have perfectly visible sprites on various backgrounds, just as long as you colour sprites differently from backgrounds.

Again, great in an ideal world...but if a publisher says "Here's our White Ninja.  We want him to run around 12 snow levels.", you have to come up with some way to solve that and please the publisher. 

in my mind, using dark pixels around edges that would otherwise be hit by light directly is just wrong.

I think there are other possible techniques a person can use, but I find that selout is extremely versatile, whereas other techniques tend to be more based around "well if we just make our game in this unique style, we can use this method".

Anything I say is purely my opinion though. 

- Tsugumo