All guns are unsafe if you do unsafe things with them. There are millions of 1911's out there, and I don't know anyone who's had an accidental discharge. They also have a grip safety to prevent them from discharging when out of your grasp. As for the difference between single and double action, there are hundreds of different flavours out there, and the restricted course is kept very basic to squeeze everything into a day. Your best bet is to learn about the gun you want to use or own, learn all the controls thoroughly before you ever put ammo anywhere near it, and (most importantly) NEVER point a gun at anything you don't want destroyed. That last one will make this sport/hobby one of the safest things you've ever done.
You're right to approach with caution and a want for safety, but there's no reason to be frightened by a particular action or type of gun. All can be enjoyed in a perfectly safe fashion, it's all about knowing your gun and behaving in a safe manner. And as you learn, you'll probably find that your instructor isn't the be all end all of knowledge. Mine was pretty good, but I've heard some real horror stories of 'but my instructor told me'.

And don't worry too much about BR, just some friendly razzing (I think)....