You need to change this (somewhere around line 719 of jquery.fancybox-1.3.1.js):
$('body').append(
tmp = $('<div id="fancybox-tmp"></div>'),
loading = $('<div id="fancybox-loading"><div></div></div>'),
overlay = $('<div id="fancybox-overlay"></div>'),
wrap = $('<div id="fancybox-wrap"></div>')
);
to
$('form').append(
tmp = $('<div id="fancybox-tmp"></div>'),
loading = $('<div id="fancybox-loading"><div></div></div>'),
overlay = $('<div id="fancybox-overlay"></div>'),
wrap = $('<div id="fancybox-wrap"></div>')
);