Also, Anthony may not have wanted anything to do with his father's business, but I think he would have been at least vaguely aware of the fact that Michael had kept some measure of peace all those years between G2 and G3.

Perhaps through Anthony's perspective, all of a sudden Vincent shows up, everything goes to hell, and Mary winds up being killed.

In a way, Michael's hopes (justified or not) to bring the Corleones into legitimacy way back in the original movie set him on the road to hell. How tragic it would be if Anthony, simply wanting to neutralize/stop Vincent (with whom all the violence started again, from Anthony's perspective) ends up walking the same road to hell his father did.