The monk seems to be rather atypical, and “allegedly claimed that he had supernatural power and was able to tell the past and predict the future of the students.” It’s possible that he’s a charlatan, or even that he’s mentally ill.
But ideas like this do tend to pop up from time to time, and so here are a few arguments against this particular take on karma.
First, the Buddha specifically stated that not everything that happens to us in the present moment is a result of karma. He pointed to physiological and environmental factors as affecting us, as well as the actions of other people. The earlier Buddhist commentators enumerated a number of forms of conditionality that included physical causality (physical and chemical laws), biological causality (which would include things like viruses and other diseases), mental causality, karmic causality, and also a form of transcendental causality. I won’t go into all of this, but it’s clear that neither the Buddha nor early Buddhists believed that karma was the only thing affecting us. Certainly our mental states and the choices we make can affect our health, but even Buddhas get ill.
Secondly, the Buddha stressed compassion, himself took care of the sick, and encouraged his monks to take care of the sick. “Whoever would tend to me, should tend to the sick,” he is reported as saying.
Thirdly, following from this, there are ample provisions in the monastic code of conduct allowing for medicines. Our unnamed monk would be well aware of this!
Fourthly, the Buddha said that trying to figure out what’s the result of karma is an “unconjecturable that is not to be conjectured about, that would bring madness and vexation to anyone who conjectured about it.” Although perhaps it also works the other way around: that people who are mentally ill are more prone to have delusions about karma.
And lastly, if it was indeed the karma of sick people that caused them to be sick, then wouldn’t it also be their karma that brought them into contact with a doctor?
The Buddha taught compassion. He taught us to recognize that other people’s sufferings are as real to them as ours are to us. And on the basis of this we should empathize with others and seek not to cause them suffering but to relieve suffering when we can. Here’s Dhammapada verse 20:
All tremble at violence
Life is dear to all
Putting oneself in the place of another
One should neither kill nor cause another
This is the Buddhist version of the Golden Rule.
And in the Saleyyaka Sutta the ideal practitioner is described like this:
Now I’m sure that this monk would argue something like “it’s more compassionate to let being suffer from sickness because it allows their past karma to come to fruition,” but a view like that is very far from the kind of compassion that the Buddha advocated.
There is the case where a certain person, abandoning the taking of life, abstains from the taking of life. He dwells with his rod laid down, his knife laid down, scrupulous, merciful, compassionate for the welfare of all living beings.
In a conversation on Google+, Denis Wallez (who pointed out the corollary that is karma determines everything then it brings sick people into contact with doctors) suggested that the antidote to such gullibility (thinking here of the medical students rather than the monk) was to get people to read more of the Pali canon, which contains (as you’ll see above) ample evidence to contradict the idea that the sick do not deserve treatment, and more importantly to encourage critical thinking. The Buddha himself, in the Kalama Sutta, famously encouraged us not to believe something just because some monk says so!