Validator does not report improperly terminated tags

The attached document was submitted by a student of mine.  It includes paragraph tags that are terminated as empty elements, and as such, I 
don't think it should be considered valid under the strict DTD.  Nevertheless, the w3c validator reports it as valid.  Validator.nu does 
report the improperly terminated paragraph tags as errors.  

Is this a bug or is it something I don't understand correctly?

Thanks for your help.

John Kozma