the file you have sent is a little differant than the one on your web site.
the one on your website that you are saying does not validate the captcha is set to post to another page:
<form action="http://www.cancersupport.ch/cgi-bin/formmail.pl" method="post" name="ContactUs" id="ContactUs" >
if the forms action is to go to another page, the captcha validation code will not have a chance to execute.
for captcha to validate properly, the forms action must be set to post to itself:
<form action="" method="post" name="ContactUs" id="ContactUs" >