You've got me wondering this now, too. We have used copper in our birdbaths for a few years now and haven't noticed any issues.
Our water pipes in the house are also copper. So when we water or drink, it comes through copper tubing.
My inclination is that it would require some other catalyst to make the copper available in a way to poison, and I am not educated enough on the subject. I'll give major acorn tips to anyone who can provide a definitive answer to this.
