4.01 validation inconsistency re: <p> in HTML 4.01

 I submitted a web page for verification to
http://validator.w3.org/file-upload.html.  It reported that:
	  This Page Is Valid HTML 4.01 Transitional!
...and stated that I could add the following HTML to the page.
 
    <p>
      <a href="http://validator.w3.org/check/referer"><img border="0"
          src="http://www.w3.org/Icons/valid-html401"
          alt="Valid HTML 4.01!" height="31" width="88"></a>
    </p>

I did so, and then the page would no longer validate -- it complained
about the <p> directive.

Removing the <p> and </p> resulted in a page that validates.