My interpretation of the note would be " better for the homeowner to put the work in before it becomes inaccessible",IOW, "should" doesn't mean "shall" or "must".

My local building code officials informed me that I could not install HVAC vents in the unfinished basement unless I pulled the permit for finishing the basement. And that I couldn't pull a seperate permit for the basement, I'd have to add it to the original house permit (we were in the middle of the original house construction) and complete it before a CO would be issued.

So we oversized the furnace and compressor, and just live with a noisy HVAC until we get them back out after the CO to complete the basement ductwork.

We also couldn't install the full electrical until we pulled that permit as well.

Weeping, wailing and gnashing of teeth.

He is probably considering the basement as 'finished space' since you have the vents etc. You need to meet the finished space coding.
You are within your right to request a code reference for anything he flags.

If he considers this finished space, does this apply to everything else? Do I need to drywall it etc if I did do electrical rough? Also would the county/city consider it finished space and tax it?