The problem is it has security restrictions that prevent you from adding digital signature fields. If the form included digital signature fields, you would be able to sign them.
I wouldn't say it's an error, but do agree that it's confusing. When deciphering the restrictions summary, you have to consider what usage rights are present, the restrictions that are applied through standard password security, the native capabilities of the viewer (Acrobat vs Reader), and the objects that are present in the document. Even though it shows that signing is allowed, what it really means is signing of existing digital signature fields is allowed, but since there are none, it really isn't. You are prevented from adding digital signatue fields by the password security that was applied. If you knew the password, you could remove the restrictions and would then be able to sign.
George is correct and I do agree that the Restriction Summary is confusing. If we can set aside the usability of the Document Properties dialog for a moment, the real problem here is when the document author added the form fields to the file (which had to be done prior to when they encrypted the file using Password Security) they did not add a digital signature field in either Section 9.b or 15.d, but rather added a text field. Had they added the correct form field type you would have been able to click on the field and add your digital signature after you removed the Reader Usage Rights (that what happens when you do the "Save a Copy" operation).
It is certainly possible that this organization doesn't recognize a digital signature as a valid type of authentication because not only did they neglect to add a signature field, but also resticted the use of digital signatures when they Reader Enabled the file. It could just be that the DoD want you to print the file and sign it by pen (aka a "wet ink" signature) and they won't accept an elctronic or digital signature.