Why is that absurd? Your historical point at Africa actually aids in the belief that this could be some type of judgment. The “voodoo” countries of Africa are in as deplorable condition as Haiti. Coincidence?
Proving a negative is possible, it just makes for a poor argument in most situations. When the argument is based on faith, such is much easier; for example, the statement that those who fail to accept Christ will not go to heaven. This statement can be proved by references to the Bible and it is a negative. It requires faith, but that faith proves a negative.