The comment said specifically "Major" accidents within specific time frame. I don't see anything in your link contradicting them. The claim was not that there were not any accidents.
Ok, then let's define it. There is a world of difference between Part 121, Part 135, and Part 91 operations. Almost no one in America will ever be on a 135 or 91 flight. If we limit ourselves to 121, which is what we're actually talking about when we talk about air travel, then you've got Southwest 1380, and before that you have to go all the way back to Colgan.