I am thinking at it from this point of view, say you create a library named libmath and you put a function in it named add. Then someone makes an app that uses your libmath named MathApp.

If I reimplemnt libmath myself, then do some trickery to make MathApp use my version did I emulate your library or reimplement it? IMO I reimplemented it and it is very possible that my implementation could be less buggy and faster in some cases.