Maybe the file is secured or does not allow adding comments or filling-in form fields...
Well the form is degined to be filled-in, so that would be odd. I don't see any 'protection', but how can I check it to be 100% sure?
Go to File - Properties - Security and check what is allowed and what is not allowed there.
This will also happen if you open a form with actual form fields in the "Fill & Sign" tool, the existing form fields can be filled out inside of Fill & Sign or just in Acrobat/Reader outside of the Fill & Sign tool, but any PDF with real "field" (Acroform or XFA) will not show the tools in Fill & Sign to add text fields and checkboxes etc. Fill & Sign can still be used to add a simple signature to an Acroform and you can just click inside the highlighted fields (should be highlighted) to add information.