I certainly can't rule out freak accidents. However, I think that both speed and situational awareness make a difference on a bike. I tend to notice things that come into my field of vision, with plenty of time to react. In fact, I probably steer clear of things like debris and potholes on virtually every ride.
The reason why I mention congestion is threefold. First, getting hit by a car is by far the predominant hazard. I consider avoiding cars to be the #1 safety measure for cycling. If you take away that factor, then I doubt that cycling is more dangerous than driving. Second, beyond a certain level of congestion, drivers are not fully in control of their cars, but are controlled by the pace of traffic. Third, dodging traffic is the primary distraction that would make a cyclist fail to notice something like debris on the road.
I'm lucky to live in a town that has a network of bike paths, bike lanes in the more dense areas, and ample routes along sleepy residential streets. I encounter very few cars, and don't have to mix it up with heavy car traffic. Granted, living in a mid-sized town doesn't solve the car problem for humanity.
Edit: Re-reading our posts, I realized that I should clarify. "Bike" is a pedal bike in my case.
Also dangers are easier to avoid on a bike provided you are going at reasonnable speed because your own vehicle is smaller. The biggest danger is target fixation but that is something riders need to train against.
Obviously training both of riders and drivers vary a lot between countries and that is where lie most of the problem as well as considering that driving/riding is a right and not a privilege accorded to people serious enough to operate vehicles safely. I find it completely insane that some countries like the USA allows kids to drive with barely any training. IMHO before 24-25 year old, there are very few adults that are mature enough to drive safely. I also fThat is probably ind insane that a country allow people to buy, rent and drive a vehicle after more than 2 DUI convictions. That should lead to a lifetime ban.
I became a motorbike in my late 30's and I see I am not taking risks like a lot of riders around me. I am taking ample distance between me and cars, act as if I was invisible and other users would do the most insane thing possible at all times and don't swerve around vehicles. I am even slower descending a mountain pass on my motorbike than I am riding my road bicycle.
I know from my experience driving cars at the same age that it would have been totally stupid to let 20y old me ride a motorbike.
OTOH motorbiking would be much safer with less cars on the road.