"Alternative medicine" covers a pretty broad field, so it's hard to make accurate generalizations. We seem to be drifting toward herbal medicine in our discussion, but there is a lot of other practice that would fall under the heading of "alternative".
Rik, you analogy, though funny is a good illustration, and Ironman summed it pretty well. Here's a "natural substance" that has an ingredient that has a real effect on the body. Is it better to just consume the natural ingredient, or is it better to pay lots of money to buy the refined, or even synthetic version of that substance. For me, it depends on many things. How important is it to take anything for the problem? Like taking something "to improve liver health" when there's nothing wrong with your liver. Lots of people take meds that they don't strictly need (I could rant about that). Then, how much evidence is there that the "natural" stuff helps. It's hard to finance research into something that anyone can get from their rabbit hutch, or pick in their garden, but there are a few non-profit organizations that do a little of that sort of work. The studies tend to be small, and not statistically powerful, but there is some research, more as interest increases.
Another factor is how crucial is the dosing. For some things a wide range is safe and maybe effective. For some medicines there is a very narrow "window" of dose that is effective and still safe; less doesn't help, more causes problems. Herbal products are hard to control precisely.
Also, the reality today is that people are turning to herbal (and other alternative medicine) because of the high cost of conventional medicine. Someone who is poor, has little or no insurance, and thinks that an herbal product might help a medical problem that they have, is very tempted to try it, and it's hard to blame them.
Herbal medicine products are hard to control for concentration. If you are going to take rabbit poo, should you be concerned that the poo of black rabbits is 3 times stronger than the poo of white rabbits, and the local farmer's rabbit herd is a mix of both? Rabbits who eat clover produce stronger poo that those who eat grass, and the local farmer feeds his rabbits Purina Rabbit Chow, and the content of clover is unknown. The age of the rabbits and the amount of time they spend in the sun also affect the strength.
Herbal products are not regulated. When you take rabbit poo, you have no guarantee that the workers who bottle it up even wash their hands before working on the production line. They might handle your rabbit poo with dirty hands! No one regulates the storage conditions, etc.
There's a list of 15 or 20 herbal medicines that are known to have some usefulness. Some doctors now are practicing what they call "complimentary medicine", educating themselves about herbal (and other alternative practices), and incorporating it into an otherwise-conventional practice. This satisfies many people who are interested in alternatives, but want to combine it with the tried and true.
For some conditions it might make a measure of sense to try an alternative practice for a time, and if it's not helping turn to more conventional methods. For some conditions that would delay effective treatment. For example, a man with prostate problems, checked by a doctor to rule out cancer, might try taking the herb saw palmetto, which has been shown to reduce hypertrophy of the prostate and is relatively safe. If he is getting good results (easier to pee, getting up less at night, etc) fine. If and when symptoms progress, he can start taking conventional drugs, and nothing lost.
On the other hand, if you have cancer, trying herbs (which haven't been shown to help) while the cancer grows is (in my opinion) crazy.