In economics things are never as simple as they seem. Take for example the brain drain of African doctors. Michael Clemens of the Center for Global Development describes in his blog about a study he published on African doctors working abroad. He was concerned that his study, which as I see it was intended to measure the number of African medical professional working abroad was being used to show brain drain is a problem in Africa.
In light of this perceived problem England has decided not to pursue African trained doctors. However, that might be the right strategy as Clemens shows in another paper that being able to migrate actually increases the number of people who enter the medical profession in these countries. In other words if you increase the expected wage with the opportunity of foreign work, then more people train to be doctors.
As he also points out African health professionals can earn 5 to 10 times their salary abroad. If large remittances are being sent back home it is possible that the money sent back might do more good then the doctor could have in their own country.