I admit I haven't read all the replies.
I just wanted to jump in with [another] story about why people (kids or adults) should always ask before petting a strange animal at the vet.
I had an awesome cat. She lived a long happy life (20+ years!) and was relatively healthy throughout, maintaining a lovely coat to her last day. She died at home peacefully. I placed her body on her favorite fleece throw and took her to the vet's to be cremated. I held her body on my lap, half wrapped in her blanket. Much like a person who has died peacefully, she looked fine,and because it had been about a few hours, rigamortis had set in and she wasn't limp. Because I loved my cat, as I sat waiting to be called up my a vet tech, I stroked her head a bit.
A kid came up and asked if she could pet my cat. Its a good thing she did ask, since I had to say "sure, but just so you know, she's dead."