They did one of these on CSI once, and AFAIK they base their shows on real cases or things that are possible...
Off topic, I know, but whenever you describe CSI as being based on reality in any way I have to stop you. On CSI I've seen a murder get solved by the detective taking a point and click digital camera from a tourist who was taking a picture of a group of their friends, then zoom in on the EYE of one of the friends, in which they could clearly see the reflection of the murder happening. Right.
Then there was a CSI Miami in which a person attempted to murder a cuban immigrant, overhearing the beach he was going to land at, rushing out ahead of time and planting a SINGLE landmine, which the intended target actually stepped on. Right.
Back on topic: I'm sure it's entirely possible to accidentally cut off your head. One of my distant cousins cut off his foot with a chain saw. the concept of the decapitation not being suspicious, while amusing, is entirely plausible to me.
~Jason