I think the guy has a point to a degree. It's not that CF is unsafe for bike componets. But making componets very lightweight has its tradeoffs, and given that most CF components are made to be very light, they're going to fail more often than a well engineered heavier componet.

The discussion of CF handlebars on Competitive Cyclist's web page puts it pretty well:

Are carbon handlebars safe?
The short answer is "yes", although the longer answer is a little more complicated. For some reason, as an industry we've become fixated on the weight of handlebars. It's as though breaking the 200g barrier will allow an average rider to suddenly contend for an alpine stage of the Tour de France. This, of course, is not the case. It's an irrational obsession that has serious ramifications in regards to the care and feeding of your bike.

A lot of very nicely made & very thoroughly tested carbon bars exist today. We need to accept the fact, though, that carbon bars have their Achilles heels. For example, you clamp aero bars to only one or two carbon bar models on the market today. Most aren't built to withstand such clamping force. And while carbon bars can handle unbelievably forces pushing downward on the tops or the drops, they aren't as robust in terms of the side-loaded forces a bike has to withstand during a crash.

If you're trying to build a tricked-out, superlight bike are carbon bars appropriate? Yes indeed. But ask yourself something: Why is it when you watch the video of the Tour de France you don't see a single rider with carbon handlebars? The answer is rather easy: Pro mechanics are big believers in due diligence. They know that if one of their riders crashes (and they all do), or if they accidentally drop or tip over a bike when loading it or unloading it, the handlebar takes the brunt of the force. In either situation prudence requires at the very least that you unwrap the bars, remove the STI or Ergo, and remove the stem to closely inspect the bar to ensure that no micro-cracking occurred as a result of the mishap. Such due diligence, of course, is an enormous pain in the ass, and sticking with an alloy bar that weighs in at 20g heavier is the sensible solution.

An engineer at FSA summarized the carbon bar situation very succinctly. He said that if the consumer demands F1-quality componentry, they need to have an F1-type mentality about it. How expensive are the composite components on an F1 car? Outrageous. How many races do most of those components make it through? Oftentimes one only. The notion that such components are built to last as long as a well-made carbon or alloy frame is simply wrong and misses the point entirely. Carbon bars, like carbon rims, are made with pure performance in mind, i.e. durability isn't paramount.

So, to answer the question, are carbon handlebars safe? Yes they are. But if you crash them, or otherwise submit them to odd side loaded forces (such as having your bike tip over when leaning against your car or garage wall), do everyone a favor and replace them.