It is an urban myth that carbon is inherently unreliable over time and prone to failure after any minor mishap or impact. This has long since been shown as incorrect. There are millions of carbon forks out there and if they were prone to catastrophic failure manufactures would be bankrupted from the costs of litigation and settlements. If a fork can be reliable then a frame can be also. If pictures of failed frames are what you are looking for, this applies to all material types. Just google failed titanium bicycle frames and look at the images tab.
With some manufacturers electing to build ultra-light frames, reliability becomes an issue, try building an 800-gram titanium bike and let some pro tour riders beat on it for a season, let's see how that turns out. If one likes titanium great enjoy your bike but to say carbon bikes are crap and unsafe is silly.