There is nothing about that document that qualifies it as being " 'interactive' - like a form to fill in". As you say,
and that shows in its structure - it's not a particularly good conversion. There are lots of unnecessary frames and other graphic object in the document - and the frames are what's causing "a whole other section gets greyed out" when you tryi to select some content.

You might do better opening the pdf directly in Word. Without knowing what Word version you're using (your user profile says Office 2003 or Windows XP, which is highly unlikely), more specific guidance can't be given.

Kindly update your user profile to reflect the actual Office & Windows versions you're using.

__________________
Cheers,
Paul Edstein
[Fmr MS MVP - Word]