Why is some metal safe to use in a microwave, but others not?
Metal on its own doesn't necessarily cause electric discharge in a microwave. 

What causes the sparking that you see when you put a fork in a microwave is due to the "sharp" edges of the fork. These edges concentrate the voltage at their tips which will cause a spark when it exceeds the dielectric breakdown of air.

Things like sheet pans (with rounded edges), or rounded metal racks are used frequently in microwaves with no ill effect. The absence of any pointed edges allows this. The rim of your bowl fits this requirement.