Jim,I do not Know,about flat stem on Sicilian white,but I know some cultivars do have flat stems on the fruits,it is not unique to your fig.
I did not keep Sicilian white for too long,because it waas behaving just like the fig described in this topic,it can't take rain while it is ripening.
Similar figs to Sicilian white and same problem,i had with Brooklyn white,and Genoa white,and so I think they are the same,and I discarded them all.