Will natural resources lift Africans out of poverty?

Africa is blessed with a fair amount of natural and environmental resources. Access to these resources by the rural poor is often  seen as a way to lift Africans out of poverty.  This way of thinking is illustrated in the next diagram from UNEP/Grid Arendal:.

The reasoning is as follows : 

The rural poor of the World, and the poor countries that they live in, do not have much in monetary wealth - but natural resources represents a possible source of income. With the right support, on both the national level as well as from the international community, the economical growth generated from these resources can alleviate poverty sustainably.

Every word of the above I can relate to, but why am I not convinced? Have this not been tried in Africa for decades? What's different? 

Transparent and accountable governments are needed to keep the resource curse at bay (see earlier post on Paul Collier's Bottom Billion).  Innovation, creativity and the space to compete on level playing plays are needed to make rural poor really unlock the value of these natural resources or just be caught in another (often externally designed) survivalistic poverty trap.