I am referring to NA accents, not worldwide accents. "Normal" simply means the majority. Nor am I implying it's bad to not be the norm. A Spanish accent is normal for Spaniards, an English accent is normal for the English, etc.
The majority of NA residents whose first language is English speak normal, which is without an accent. An accent is a specific way of speaking. Pronunciation of certain words does not necessarily equate to an accent, although an accent CAN effect the pronunciation of a word. If I say tomato and tomata, my voice emphasis is not going to change, but the pronunciation is. Therefore, I do not have an accent just because I pronounced a word differently.