Our trees in Sicily do drop their leaves in "winter" but they never truly go dormant in the way they do where I live in Canada. That is to say, in Sicily the sap never really stops flowing. They seem to go into a protective state. Here in Toronto the trees (especially in pots) usually screech to a complete halt.
I admit I've never given much attention to chill hours... but I figure even in south TX.... it shouldn't be too warm for fig trees.
@ETXfigs - I gave an LSU Purple to the son of one of my friends a few years ago. He was really getting into growing figs. He put it in a west window of the house with plans to move it... it set and ripened so many that they decided to not fix what's not broken.... now the tree sits in a west window and produces flushes of figs all year long...