Welcome to ECN forums.
Based on what you said, having an electrician 'check' was a good move. That said, I have an issue with the 'open' boxes, and how they were not corrected by either the original installer, noted by the 'inspector' or required to be covered by the 'electrician'.
Again, I would make a phone call to the Chicago area AHJs office and ask if there are any local codes regarding the insulation cover over the boxes. The NEC is moot on this subject.
