It was news to me as well. I thought brake fluid contamination was a concern primarily because of ABS modules, figured it was because of moisture. Apparently that's not as much a concern anymore. The copper comes from the brake lines indicating a breakdown of the brake fluid additive package. Didn't even know it had a additive package.

Diagnostic fees wasn't even a term when I was a mechanic in the 1970's. Never heard of it until the 1980's. The quoted fee sounds high to me to put it on a lift, pull the wheels and drums if any. 20 minutes work? I think my record for 4 tires and balance was ~ 45 minutes back in the day.

The shops attitude when the work was declined was the only thing that bothered me. That's not how you treat a customer. It's not like the pads were gone and riding on metal or tires down to the cord. Nothing imminently dangerous here.