Go on, convince me...

No misunderstanding on my part. I know exactly what a fixed wheel is and I know they can have brakes. I also know you can crash on them, just like on any other bike. Maybe the question should be are you more likely to?
Controversy? maybe, maybe not, but there's nothing wrong with a healthy debate is there? I'm sure we'd all agree that the most important thing is we just ride and enjoy it what ever we're on :-)

You read a breakless bicycle rider having an accident as "not a good advert for the fixed wheel."

I don't think I am being unreasonable in thinking that your prejudices against fixed wheel are based on a (common) misunderstanding.