That's simply not true. The grid operates with accordance to guidelines set by the North American Electricity Reliability Commission (NERC), one of the policy is something called "N-1 Criterion". Which means any one single transmission line or generation unit can go down without affecting the grid. And NERC also requires that the operator balance the grid to satisfy N-1 criterion after one contingency happens. So it's not like once one unit trips, another unit trip would destroy the grid. Yes, balancing the grid after a contingency takes time, but the likely hood of 2 events happen so closely is low. Plus, the N-1 Criterion requires the grid to remain stable for the single WORST scenario, which many contingencies aren't.
The cause of the August 2003 blackout also was caused by improper procedure by FirstEnergy, along with lack of situational awareness on the grid. The joint task force report on the blackout concluded the blackout could have and should have been prevented by proper operating procedure. You can find the link to it at the bottom of that wiki page you linked to, or here: https://reports.energy.gov/
Yes, electricity travels fast, but that doesn't mean the grid is not operated to handle failures. BTW, this is my current research area, so I know at least a little bit of what I'm talking about. Not to make the logical fallacy of appealing to authority or anything.