The New York Times has a peice (which will soon vanish) Donor Mistrust Worsens AIDS in Zimbabwe. Because of corruption and government misappropriation of aid for political uses, numerous donors are declining to help at all.
This is a tough one. Corruption is a problem everywhere; some places much worse than others. Clearly if 100% of aid money is siphoned off, there's no point whatever in trying to help, since you can't. What about if 10% is siphoned off? That's probably comparable to normal costs of doing business. What about if 50%? At that point you can help 2 people somewhere else for the price of helping one person in the corrupt region. If the problem is world-wide, you can help more people by going elsewhere; and I think you probably should. If the problem is local, then I guess you have to go ahead anyway.
But there's more than corruption at issue here. The government lets aid flow to supporters, but not to tribes that are political opponents. There isn't even the weak excuse of civil war. People often try to interdict supplies to people fighting them. But that's not what's happening.
When can you restrict aid? If it is a matter of cost, traditionally you can restrict it to those able to pay for it. By convention money represents a promise of goods or services, given for value received. Maybe the money was stolen, but trying to untangle such history is fraught with opportunities for abuse, so we just assume that someone is rich because they deserve it. So someone rich enough to afford health care presumably deserves it. (I hear peals of laughter. I don't hear better schemes, though.)
But if the aid is essentially free, how can you deny it to honest citizens? The aid group will no doubt help some people who would otherwise have died, but will be simultaneously making themselves complicit in the government's evil work by deliberately denying help to others.
It is a cop-out to say "honest people can disagree" without suggesting how somebody can decide the issue for themselves. One rather selfish way to look at the question is "what becomes of you?" If you can acclimate yourself to the situation, run away and don't look back.
In some places in the ante-bellum south slave owners did not want Christian preachers to have any contact with their slaves. Others thought it good provided the preachers emphasized the passages about slaves obeying their masters and slid by the passages about equality before God. Some churches agreed to the compromise, arguing that the inestimable value of the Gospel for the slaves outweighed the injury caused by leaving out some minor details. And I think this proved true, for the slaves eventually found out about the whole story anyway. But the cost for those churches was high: they became acclimated to and eventually staunch defenders of the status quo of slavery.
Another question is "can you communicate your concerns?" The answer will almost certainly be no. Can you live with that?
Pray. One person may be called and other not, or called only to work there for a while. Pray.