I think the doc should be considered correct and posixpath buggy.  The ntpath code checks for the existence of HOME and substitutes before returning the arg unchanged, as documented.

    if 'HOME' in os.environ:
        userhome = os.environ['HOME']
    elif 'USERPROFILE' in os.environ:
        userhome = os.environ['USERPROFILE']
    elif not 'HOMEPATH' in os.environ:
        return path
    <create userhome from HOMEDRIVE and HOMEPATH

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The pwd doc already says " KeyError is raised if the entry asked for cannot be found.", so this is not an issue.