If the PDF lacks form fields than it is not a "fillable" form for digital processing and return.
Rather, it is meant to be printed, filled in with pen, then mailed back or scanned and the scanner output image mailed back or the completed paper sent back by fax.
To support use with version of Adobe Reader before Reader XI a PDF (that has form fields) had to be processed by Acrobat Pro to place special permissions that let earlier Reader users enter information and save that with the PDF.
Users of Adobe Reader XI do not have to deal with that particular issue.
Suggestion: contact the PDF provider and discuss the issue with them.
(Hey, a may be a lert test!)
Be well...