On the episode of All That when Britney Spears sings "Oops I Did it Again", watch at the part right before the first chorus. Well, it is already obvious that she is lip-synching, but it is even more obvious because they do a close-up on her mouth and she says "but" instead of "and". She makes it so obvious!
Britney Spears always lip syncs. She's a pop star. That's what pop stars DO. If you want to watch something where the people singing aren't totally fake, go watch a rock video, even though I'm totally opposed to videos in general (music is for the ears, not the eyes.)
The singers on All That and Nickelodeon always Lip Sync! Haven't you ever noticed that when they perform, it sounds exactly the same as when they sing it on the CD? Plus, they never bring any instruments with them.
Artists always lip-synch because they can't dance while singing. They are dancing and lip-synching over a recording of their own voice. So this is really not a particular slip-up.