So, this is a recurring issue in the Shakespearean canon:
I know Elizabethan medicine wasn't exactly state-of-the-art, but I'm constantly appalled at how readily people jump to conclusion of "Oh no, she's dead, let's dump the body somewhere" after someone falls over. Then again, these are the same people who say "You know, it's remarkable how you, a boy, look exactly like a girl, but are, in fact, totally a boy".
What I'm saying is that Shakespeare's characters are criminally unobservant. That's what I'm saying.