[throwanem]

Which government has recognized ISIL's claim to sovereignty in those territories it still holds, or indeed in any territory at all?

[vacri]

The US and Russia both have claims to sovereignty there!?

[throwanem]

ISIL's claim is the one under discussion, though. That's the one whose recognition would signify in the question of whether their actions are legitimate warfare, by the standard cited earlier in this thread. US and Russian claims are a different question altogether.