I could not find where in the paper there was the absolute conclusion which you stated. I did however find these points, some of which bolster my latest hypothesis;
what is your hypothesis Mm?
here is another paper, i cant quite find the one that first convinced me about it but will keep looking.
"Phosphorus release from phosphate rock and iron phosphate by low-molecular-weight organic acids."
http://www.ncbi.nlm.nih.gov/pubmed/14971442