You can NIW or EB1 at the same time, or NIW first, then EB1. That is the normal way people do.
Sometimes people got both approved, sometimes NIW got denied or RFEed while EB1 approved, soemtimes EB1 got approved and NIW denied/RFEed.
The immigration story you mentioned may be true in the past. Under current situations, I do not think there will be any officers who will ask such question again. Your concern sounds resonable. You can do whatever you feel comfortable.
Just for your reference!!