Did you get to taste it when the figs were ripening, or are those not your pictures? Seems like that tree does well in your area, but if the figs are insipid then that doesn't really matter.
I don't know if it's a BT or not. The leaves on the California BT I had didn't look like that, but the figs on the tree pictured do look similar to a BT. If nothing else I would see if you can taste them at some time and if you like them then that's all that matters. Right?