Maybe those are hidden fields, which according to HTML::Form (used under the hood) start out readonly:

This method is used to get/set the value of the readonly attribute. You are allowed to modify the value of readonly inputs, but setting the value will generate some noise when warnings are enabled. Hidden fields always start out readonly.

Update (in reply to your update):  have you tried turning off the readonly attribute to see if it helps?  (IIRC, $mech->forms returns HTML::Form objects, whose inputs method returns input objects, upon which you can then call the readonly method...)