No. At least, not any more than a football player getting paralyzed by a vicious hit is "football's" fault. Which is to say, participating in a dangerous activity carries with it the risk of serious injury. Kevin Ogar is, sadly, one of the unlucky ones. If anything good can come out of his case, it may be that it gives all the Crossfit weekend warriors a reason to pause and evaluate exactly what they're doing.
Ogar was, by all accounts, extremely strong and experienced. His injury occurred while performing a snatch, in which a lifter pulls the barbell from the ground to overhead in one explosive movement. The snatch is a staple movement of Olympic weightlifting. It is great for building explosive power. It is also one of the most dangerous exercises that you can do in the gym. Olympic weightlifting (as opposed to regular old weightlifting) is characterized by these explosive movements, where the lifter must generate a burst of energy to move the bar into position with great speed. This speed element narrows the window for error, increases the risk of injury, and makes the use of correct form incredibly important. A fast-moving bar with weight on it, improperly handled, can easily tear a rotator cuff or wrench a back. Worse, a small miscue on the snatch can cause the lifter to fail with the bar overhead, and it can fall down onto them, and if they can't get out of the way in time, what happened to Kevin Ogar can happen to anyone.
Crossfit workouts often add another element of danger to Olympic lifts: pressure to do them quickly. Crossfit often asks athletes to do the maximum amount of reps they can in a set period of time, or as many rounds as possible of several exercises. Olympic lifts are dangerous enough (especially for people who haven't spent years practicing them) in a perfectly calm environment. Doing them in a competitive environment with time pressure adds to the risk of injury.
There are plenty of great weightlifting moves like squats and deadlifts and presses and rows that provide great benefits and do not contain the speed element that makes Olympic lifting so risky. If you are not a high-level competitive athlete, you can probably stand to not do Olympic lifts. Particularly not timed Olympic lifts. The fact that Crossfit encourages thousands of poorly trained people to perform Olympic movements as fast as they can is probably the single worst thing about Crossfit, besides the socks.
You can donate to Kevin Ogar's hospital bills here.