Stop trying to write into the stdlib during packaging tests (#12331).

This prevents tests from failing when run from a Python installed in a
read-only directory.  The code is a bit uglier; shutil.copytree calls
copystat on directories behind our back, so I had to add an os.walk
with os.chmod (*and* os.path.join!) calls.  shutil, I am disappoint.

This changeset is dedicated to the hundreds of neurons that were lost
while I was debugging this on an otherwise fine afternoon.

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