I agree, there are tons of bacteria found in birdbaths and regarding drowning in an inch of water; it is possible:
http://www.thejournal.ie/baby-...
http://www.nhwatersafety.com/d...
http://www.realhomesafety.com/...
From one of the above sites:
Young children can drown in as little as 1 inch of water. That means drowning can happen where you'd least expect it - the sink, the toilet bowl, fountains, buckets, pet bowls, birdbaths, wading pools, or small bodies of standing water around your home, such as ditches filled with rainwater. (Source: KidsHealth/The Nemours Foundation, June 2004, Most Kids Who Drowned Were Supervised, Study Finds)