'Filtered HTML' setting has no effect on CKEditor fields

Hi, my customer pasted a bunch of iWeb source code or somesuch into the CKEditor on a CCK Textarea field, saved the node. The Input Format is set to 'Filtered HTML'.

All of the span tags look like this:

<span class="Apple-style-span" style="font-family: Trebuchet,'Trebuchet MS',Arial,sans-serif; line-height: 20px; font-size: 13px;">

They're all over the text. Again, the format is set to 'Filtered HTML'. This shouldn't be happening.

Does CKEditor override Drupal's core filters? Do I have to install one of those contrib HTML filter modules to control CKEditor's filtering?

Thanks.