I guess it doesn't seem too hard to define, but maybe the confusion is philosophical. When I say bit-for-bit, that's what I mean. When I say "remake" it involves using your own voice and instruments to make a new recording. That's actually been the default through all history. There's no "original recordings" for Beethoven's music. If you buy a pop song's sheet music, never having heard the song, that's a very traditional kind of making music, and completely appropriate.
But really, philosophically. Here's an original recording (couldn't find the studio version):
If that second video is were the Verve stole their sample then I think there's was sufficiently different as to be new. It wasn't a real sample, not like "brush your shoulders off" ...I just heard that for the first time because of this story. I was getter mad just listening to it.
But really, philosophically. Here's an original recording (couldn't find the studio version):
http://www.youtube.com/watch?v=BzZHmHqEE7k
Okay, and here's a great remake. I say great because it's so completely original at the same time:
http://www.youtube.com/watch?v=cVuh1Ymve2I
And here's a ripoff (sort of. The sampled parts were paid for), which you probably already guessed:
http://www.youtube.com/watch?v=Zx3m4e45bTo
I really like that song, but that guy added very little to the original remake, so to speak.