Many medicines don't actually treat the problem, they just treat the symptom. For example, some medicines may reduce a fever without actually treating the sickness. If you have a viral infection, the last thing you want to be doing is reducing a fever without taking some precautions against the actual virus.

A friend of mine actually died because of this. He had a fever. His parents gave him panadol to reduce the fever. When that didn't work, they went to a herbalist and got a stronger herb to reduce the fever. After a week, he suffered organ failure and died. The doctors performed an autopsy and he actually had dengue fever. Dengue fever is not fully preventable, but it certainly is treatable and deaths are rare. This was a senseless death because his mom believed the herbalist would "cure" her son of his "bad heat".

Even your basic pain medications do not stop the cause of the pain - they just prevent you from feeling the pain. Anesthetics during surgery work the same way. Cold medicines, fever reducers, most of the medications we take (especially over-the-counter ones) do nothing but mask the symptoms so that we can continue to function while our bodies make us better on their own.

For example, hydrocodone is often used as a cough suppressant in cases where the patient cannot get sufficient sleep because of coughing fits:

Hydrocodone is a narcotic cough suppressant (antitussive) that works on certain centers in the brain to stop the urge to cough... These products do not cure or shorten the length of the common cold and may cause serious side effects. To decrease the risk for serious side effects, carefully follow all dosage directions.

It's not curing anything, just making life liveable.

The statement that modern medicine fails at "treating the entire problem" is actually a true statement by the alt-med practitioners (at least in the case of the common cold), and the consumer is then allowed to draw their own incorrect conclusion that alternative medicines DO treat the entire problem. Unfortunately for alt-med practitioners, they do not have evidence on their side showing any efficacy of their products beyond the placebo effect.

Both of the previous answers are good, but it's also worth mentioning that usually this kind of argument from an alt-med source is a wedge to drive some mysticism and bunk into the mix. They are likely to profess that there is some woo behind the scenes that needs correcting in order to really solve the problem, beyond the scientifically accepted cause of the symptoms (which may or may not be treatable, and may or may not be known to the hapless patient seeking help). You know the sort - balance your auras, straighten your chi, purge the toxins, chelate the heavy metals, adjust the humors, etc.

It's a kind of god-of-the-gaps of medicine: since scientific medicine doesn't know all the answers or can't treat the "root problem" (which may or may not be true, certainly the alt-med practitioner is not going to be the best source to inform you on this) therefore there must be something else, and therefore the something else I propose is clearly the legitimate solution.

Andrew's response illustrates the danger of this approach. There may be a real, legitimate, serious medical problem, and if over-the-counter traditional medicine is not working then doctors and/or specialists need to be consulted. Relying on the mystical speculation of alt-med practitioners may well delay proper diagnosis and treatment until it is too late.