Can't find reason for Invalid Date Error

Our sitemap.xml file exactly matches Google's requirements, as far as I
can tell. I have even compared other sites' sitemap.xml files and ours
match exactly (not to say they don't also get errors). However, I'm
still getting an 'Invalid Date' error, and I'm at a loss...

http://antigua-guide.info/sitemap.xml

Does the <lastmod> date need to match the response header field
'Last-Modified' for that requested page?