Try converting your document with OCR disabled. I've seen this behavior occur a few times in the past, but never for any sort of consistent reason. To disable OCR, turn off the 'Recognize text' option prior to converting your document.
You may also want to try deleting the black boxes. It could be that they are artifacts from the original document the PDF was created from that don't actually serve a purpose.
Disabling OCR made no difference. Black boxes are still there. Though many of the pieces of the document can be ungrouped, the black boxes cannot - so they remain uneditable.
Perhaps seeing what I am attempting to explain may help...
First the Original, then the conversion.
Above is the original.
Below is the conversion:
Could you open the original PDF file and check File > Properties. I'd like to know what it says next to 'Application' and 'PDF Producer'. My guess is that it will say InDesign or Illustrator.
The black boxes are appearing behind text that has a black stroke and a drop-shadow applied to it in the authoring applicaiton. Word isn't really capable of reproducing both of these effects without using WordArt. I'm fairly positive that's what we're running into here.