This is why I'm an Objectivist - it's the only philosophy which gives a moral argument for property rights. (Most libertarian and free-market thinkers argue on pragmatic grounds, which means they are willing to compromise in the manner you describe).
Virtue of Selfishness puts the case succinctly:
"The right to life is the source of all rights—and the right to property is their only implementation. Without property rights, no other rights are possible. Since man has to sustain his life by his own effort, the man who has no right to the product of his effort has no means to sustain his life. The man who produces while others dispose of his product, is a slave.
Bear in mind that the right to property is a right to action, like all the others: it is not the right to an object, but to the action and the consequences of producing or earning that object. It is not a guarantee that a man will earn any property, but only a guarantee that he will own it if he earns it. It is the right to gain, to keep, to use and to dispose of material values."
"The right to life means that a man has the right to support his life by his own work (on any economic level, as high as his ability will carry him); it does not mean that others must provide him with the necessities of life.
The right to property means that a man has the right to take the economic actions necessary to earn property, to use it and to dispose of it; it does not mean that others must provide him with property.
There is no such thing as “a right to a job”—there is only the right of free trade, that is: a man’s right to take a job if another man chooses to hire him. There is no “right to a home,” only the right of free trade: the right to build a home or to buy it. There are no “rights to a ‘fair’ wage or a ‘fair’ price” if no one chooses to pay it, to hire a man or to buy his product. There are no “rights of consumers” to milk, shoes, movies or champagne if no producers choose to manufacture such items (there is only the right to manufacture them oneself). There are no “rights” of special groups, there are no “rights of farmers, of workers, of businessmen, of employees, of employers, of the old, of the young, of the unborn.” There are only the Rights of Man—rights possessed by every individual man and by all men as individuals."
> If a situation forced you to choose between compassion and property rights (Maybe you're asked to steal a life saving medicine for someone else in dire need), which do you choose?
The Objectivist answer is that sickness (like hunger) is not a sudden emergency but a predictable element of human life. Because of this, people invest in researching and manufacturing medicines, or studying to become doctors. They own the products of their labour, and are entitled to trade them (or donate them) as they see fit.
Many people would say they agree with this, but that there are some situations where rights should be compromised. The thing to understand is that rights are principles. In Objectivism, principles essentially encapsulate long-term pragmatism: principles are concepts you should always follow if you want good long-term results. (Rights, for example, encapsulate the principles to follow in the social realm). There will always be bad effects to violating principles, even if there appears to be a short-term gain.
If you say that one group of people (e.g., drug companies) should have their rights violated based on the needs of another group of people (e.g., sick and poor people), you establish the principle that anyone's rights can be violated for the needs of anyone else. You end up with different pressure groups and lobbyists pushing for government handouts and favourable legislation (i.e., the current situation). Linking back to the field of medicine, one practical outcome of the push to prevent "greedy drug companies hoarding medicine" has been that medical innovation has increasingly focused on things like viagra and plastic surgery, since if they develop life-saving innovations their intellectual property rights may well be violated.