By the same token, nobody can claim that medicine can heal or cure anyone.
It's just assumed that the medicine or treatment was effective, but you don't know for sure if it would not have cleared up on its own without treatment.
That depends on the condition, of course. If you are talking middle ear infections, yes. However, medical practice has been manipulated by demanding parents to give antibiotics and law suits resulting when eardrums were actually damaged without treatment.
Medical care is often nonsensical because it is driven by non-medical factors, such as business, profit motives, greed, unethical drug companies, lawyers, and soccer moms, to name just some.
FDA is under obligation to test and certify that a drug is both safe and effective before it is marketed. Obviously it is not a fail-proof system, again for a number of (complex) reasons we can discuss on another thread. The effectiveness of a drug can be demonstrated repeatedly and consistently.
As I said earlier, you are always free to refuse medical care and choose to entrust your and your family's well being entirely in the hands of God. Until someone can demonstrate reliably that prayer is as effective as medicine, I think people will take their 'chance' with standard medical care.
Most often, but not always, the reason for the effectiveness of a drug is known and quite certain. After all, drugs are specifically designed to do what they are supposed to do, to exert effect on target organ or organism, etc. based on what we know about the biomolecular structure and workings of the body. Of course, some drugs are discovered serendipitously and their mechanisms are not well understood.
You seem to make fleeting generalizations in an anecdotal fashion without ever offering as shred of evidence to support them. That's juts plain "labeling."
In one instance you are talking about the existence of evidence that something was present or absent in the case that may have been resposible or contributory. In the the other you are talking about a conclusion drawn from evidence. I wouldn't consider that "the same token".