Take a look at the IC chart here carefully.
https://d1z8zkw1yi6kd7.cloudfront.n...ures/data/000/000/211//content/class_ia-c.jpg
Notice that although the ERP is prolonged (ERP is essentially right when the plateau phase becomes slightly more negative relative to the maximum peak of the upstroke, so SOME Na+ channels are reactivated). What you can notice in the pic is that the upstroke never quite reaches the normal height, so it doesn't reach to that depolarized state at which most Na+ channels become inactivated.
However, the AP duration is the same because the slope dives down at the same time as the original via the outward K+ current.
The way that I think of it is: The more positive the cell is, the more Na+ channels are inactivated. So since the maximum peak of the upstroke is blunted and the slope is prolonged, the AP spends a longer time in the ERP, that is, the state at which the cell is depolarized enough to where you can't get a full blown AP upstroke, but to where it's slightly negative enough to have at least SOME Na+ channels available for another weaker AP.
EDIT: Although it may seem counterintuitive to keep arrhythmic cells in the ERP (the state at which another weaker AP can be generated), it's better than letting the cell hyperpolarize to the point where you can get a full blown AP upstroke. Also, by looking at the chart of the class IC, you see that even when the potential goes back to resting, you still can't get a full blown AP because the slope is blunted.
This next part i'm not 100% sure on, but here's what I think: ERP is just a term that means that not enough Na+ channels are recovered to have a full blown AP upstroke, but there are some that still can activate. So whether you have a "longer ERP" from a depolarized membrane, or by virtue of the Na+ channels being blocked by a drug, the effect is the same.
