I think you're right about the XHTML 1.0 Strict. I think W3C validates the page just for the doctype used... CSE is a little more picky...
I think it would be a good idea to use the
W3C Validator and then the
CSE HTML Validator. This way you've got two opinions.
Another validator is the one located at
htmlhelp.com but it is very similar to the W3C.