I know that they told us that their parents were killed by a firebender, and Mako witnessed it, but what if San actually survived and later became a criminal for some reason and renamed himself Ghazan? Maybe for vengeance? When Mako and Bolin are prisioners of the Red Lotus, Ghazan is surprisingly friendly with them and even plays 'two truths and a lie' one involving his moustache, which is indeed there in the only picture of his father we see.
Why didn't they recognize him? Well, Ghazan does seem damaged by 13 years of prison by wrinkles and weathered face, and his long hair and mustache gave him a different look, even comparing Ghazan to the old picture they kind of have the large chin in common
Why didn't he recognize them? Well, he hasn't seen them since they were little kids, and trying to forget the past he left behind. But maybe the reason that he is so nice with them is actually because they remind him of the sons he left behind to follow Zaheer not knowing it was actually them.
And finally, the lava bending. It is earth bending with a fire component, fit for a man who loved a firebending woman and had a firebending son. And since lavabending is so exceptional, maybe Bolin's ability is hereditary just like blood bending while it's not full moon. This would give Ghazan a backstory and it gives a very deep meaning to the scenes where he interacts with Bolin and Mako, especially their final confrontation.
What do you think?