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The piecewise implementation (well, especially the Clean Room approach) deal with how to cover your back against copyright litigation. It is not stated, that failing to do so, automatically makes you guilty of copyright infringement.
In the case of piecewise reimplementation, one very relevant issue is how significantly the code has changed. If all that remains from the original code is the function name (to assure compatibility) but the whole internal working of the function itself has changed, then I do not see how the author would not own the copyright for the change. Naturally this does not apply to minor modifications (change a few variable names etc).
The author himself states why the piecewise reimplementation is problematic:
Hence, if you rewrite the code and do not utilize the existing program structure, architecture and/or data structures, but rather rebuild the whole function (or module), then it shouldn't matter if a Clean room approach has been used or not (although a Clean room approach makes it easier to prove that the author did not rely on the existing source).
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