I'm fairly knowledgeable about knots and rope (I used to know almost every knot in the Ashley book of knots and can still tie a couple hundred from memory). There may be some knowledge to gain from a knot, but hardly what is presented.
Most people know an overhand, basic bow, reef/granny, slip knot, and half-hitch. They may cobble together a more advanced knot on accident, but that hardly proves experience. The use of climbing, fishing, or rescue knots could indicate something, but that's about the extent without going into pure guesswork.
In the butcher example, the easiest explanation is that the knot came untied, so they added a couple extra wraps to keep it together and probably had no idea it was a different knot used in a particular field.
Much more useful knowledge could be gained by the kind of rope, rope age, and wear patterns.
WRT the "knot only a butcher would know," I'm going to assume it was the surgeons knot because it is in a picture in the article and could actually be used correctly by both a butcher and binding a person. Only butchers and surgeons use that knot because it is used in cases when the rope/thread is extremely slippery as it makes it easier to keep the knot tight in those cases. No one else uses it though because it can come undone easier than a basic square knot if unbalanced as it is in the picture. So I believe that it could be an indicator that the perpetrator was the butcher.
Overall, I'd say less good than DNA evidence, better than phrenology.