Well first off I should say it's not 'my' sentence as such.Had my leg broken implies active agency, essentialy that somebody (another human being, probably) did it to you. So, grammar is OK but it's not perhaps the meaning you're after.
I broke my leg would be normal.
That's an interesting point. To remove the anthropomorphism compareI suspect it's something to do with MagdaDH's point about active agency: we expect "had my leg broken" to be followed by something which answers the question "who by". The blue sentence, by putting the accident second, at least provides a ready answer to the question "how", even if not - without anthropomorphism - to the question "who by".
Well, I would still say that I had my leg broken in a fight means one of the people who fought did it. If you broke it while fighting (eg because you jumped off a garage roof, or fell or sth) you would say I broke my leg during a fight or something along those lines.T
I was in a fight and had my leg broken.
I had my leg broken in a fight.