This is a common misconception (and one which I think reflects what the standard *SHOULD* be). Even though the close </p> tag is mandatory for certain other standards, </p> is optional in html 4.01, per http://www.w3.org/TR/html401/struct/text.htm and other w3c references:

9.3.1 Paragraphs: the P element
...
Start tag: required, End tag: optional

Whether or not this stands in the forthcoming html 5.0 standard is unknown.