My aunt's also a civil engineer, and she has a much more mundane explanation for why nails are OK and screws are not: if you use nails, someone's already calculated how many you need to ensure the structure isn't going to fall down. The strength of the nails has been calculated, their material properties are known, etc. The engineering work has been done.
If you use screws, you could have an engineer sign off on that structure (and then the inspector would let it pass), but the engineer would need to:
1) Find a data sheet on the screws you're using,
2) Do the calculations to show that you're using enough of them, and in the right places, to ensure the structure will stay standing,
3) Be willing to then sign off on the structure.
Depending on the screw, that data sheet may or may not exist.
I'm surprised your family friend didn't know this, or left that detail out of the story. Maybe he worked in another branch of civil engineering (sidewalks, sewer, etc) from structural engineering?
tl;dr: If you can pay an engineer to do the calcs (and sign off on it) to show that your screw-based structure will stay standing, the inspector won't be any problem.
If you use screws, you could have an engineer sign off on that structure (and then the inspector would let it pass), but the engineer would need to:
1) Find a data sheet on the screws you're using,
2) Do the calculations to show that you're using enough of them, and in the right places, to ensure the structure will stay standing,
3) Be willing to then sign off on the structure.
Depending on the screw, that data sheet may or may not exist.
I'm surprised your family friend didn't know this, or left that detail out of the story. Maybe he worked in another branch of civil engineering (sidewalks, sewer, etc) from structural engineering?
tl;dr: If you can pay an engineer to do the calcs (and sign off on it) to show that your screw-based structure will stay standing, the inspector won't be any problem.