HTML documents and DOCTYPE

I have a user who's hassling me because the HTML documents that I produce
with the DocBook XSL HTML stylesheets have no DOCTYPE.  I notice that the
XHTML stylesheet does list in the <xsl:output> element the information
required for a DOCTYPE, whereas the HTML stylesheet does not -- so I assume
the omission of DOCTYPE for HTML is deliberate.  Is that correct?

Also, he claims that the omission of DOCTYPE for an HTML document makes the
document invalid.  I question this, because I can find no mention of DOCTYPE
in the HTML spec at all.  Should I just ignore him? :-)