I don’t believe they falsely claim about atrocities, I can’t remember any particular such incident.
At least Kurds only fight for independence, some are mohammedans, some aren’t, and even the ones who are seem to get along with the Christian Kurds.
I might merge ISIS and al-qaeda together in this, but from the top of my head I remember them taking credit for the Norwegian mass murder that ended up being Breivik and claiming to have shot down a Sharm-el-Sheik - Petersburg plane (even posting fake video) with a missile that ended up being a bomb.
They don’t see these things as atrocities. For them claiming they did it even when it comes out as a lie is just publicity and moral boost.