Is there a flypaper effect for public health-based foreign aid?

If you give people, or a government, money to do one thing, they might reallocate some of those funds to their preferred marginal expenditures.  A recent study published in Lancet, co-authored by Christopher Murray and Chunling Lu, suggests this is what happens with many instances of foreign aid:

"For every $1 of DAH [development assistance for health] given to government, the ministry of finance reduces the amount of government expenditures allocated to the ministry of health and other government agencies that engage in health spending by about $0.43 to $1.14," they write. "From the global health community's perspective, this means that to increase government health spending by $1, global health funders need to provide at least $1.75 of DAH."

Furthermore debt relief does not increase domestic government health care spending but grants to NGOs, unlike direct foreign aid to governments, do increase such spending.  A summary of the study is here.  Here is an abstract and a gated link.