Everyone must occasionally make moral decisions. In some cases, it is right to give others help; in other cases, one should refrain. When it is or is not moral to give help depends upon the ethical system one lives by.
If one is primarily a moral absolutist, determination of right and wrong is relatively easy. If the asker is in accordance with what the moral agent considers right, help should be given. Likewise, no help should be provided to anyone whose purpose is not just. No consideration should be paid to extenuating circumstances or possible consequences resultant from the decision of whether or not to help. Such matters are irrelevant. Such is a principled but inflexible ethical system.
For those primarily utilitarian only the results of helping or not helping should be considered. If the desirable consequences of helping outweigh the harmful, help should be provided. If the harmful outweigh the pleasurable, no help should be given. Such is often difficult to determine, as various forms of "hedonic calculus" are complicated and impractical to apply to real life situations. Furthermore, utilitarianism is basically amoral, unless one equates pleasure with the highest form of the good (which is a stretch).
Those who refuse to offer help do so for various reasons. Some simply avoid responsibility, while others rationalize their decision with ethics. Such are personal matters, and generalizations about them are impossible.