The main motivation behind these changes is to rely on
https://github.com/jprichardson/node-fs-extra/blob/8.1.0/docs/copy-sync.md as
much as possible in order to avoid having to do the
`fullFilePath.replace(srcDir, '')` operation because this operation can be
error-prone.
Doing so fixes the following issues because the user-submitted file paths are
now correctly interpreted by fs-extra, closing both #6525 and #5172.