The culprit code is the following:

  (when :time-stamp-file
    (format-time-string
     (concat "<!-- " org-html-metadata-timestamp-format " -->\n")))

This `when' condition is always true, because :time-stamp-file is a keyword
and always eval to itself, never to nil.

So I think org-export-time-stamp-file should be used instead of
:time-stamp-file.