I agree that is was the parents fault. If I were the babysitter... well, actually, I'd be pretty sure it wasn't venomous or wild, just because of where I live.
But still, if there were a creature I didn't know anything about, and it was "potentially" dangerous, I think I'd be freaking out and worrying about the kids too.
And really, that's totally irresponsible not to tell her they had a snake- maybe they thought she wouldn't babysit with a snake in the house because she was too girly! Lol, but she had the guts to chop its head off.
In the end, the parents were stupid. The girl was reacting normally, and did a good job of it. I hope the snake had no pain, though if she did as good a job as it sounds, I doubt that's an issue.