Looking back, it rather surprises me that I didn't react this way when I first read the book, given that I was in a vaguely similar situation when I was ten. I got a vague warning from a dog owner, acknowledged it but didn't think it sounded serious, and got a fairly nasty (though not maiming, thank God) bite on my leg. The dog's owner promptly came over and made some comment that reeked of "I told you so" while I was on the ground bleeding.

We've got no idea what tone Draco was using with Buckbeak, but most dog owners do just what you said. "You're a stupid puppy, yes you are! Yeah, you're a stupid puppy! Aww, good dog." I could see Draco doing the equivalent of this.

At the very, very least, Hagrid needed to have the kids going up one at a time so he could supervise each individual student.