Aha.. I am using a custom postamble for html:
(setq org-html-postamble t) ; default value = 'auto
(setq org-html-postamble-format
`(("en"
,(concat "Exported using "
;; "%c" is replaced with `org-html-creator-string'
;; Emacs <VERSION> (Org mode <VERSION>)
"<div style=\"display: inline\" class=\"creator\">"
"%c</div> "
"by %e. — "
"<div style=\"display: inline\" class=\"date\">"
"%d</div>"))))
So it looks like "%d" returns an empty string if #+DATE: is omitted altogether; but if org-html-postamble is 'auto, today's date is entered if #+DATE: is omitted.