“More [sanctions] were imposed following allegations that Russia was sending its soldiers to fight with separatist rebels in eastern Ukraine.”
—When I first read the sentence, it sounded as if Russians came there in order to fight against, not alongside rebels. Of course, there were two different meanings of ‘fight’ involved—‘struggle physically’ and ‘argue’—which a native speaker would hardly to mistake, still relying on a dictionary example, “Protesters fought with the police outside the Embassy building.”, you could well be mislead reading the BBC sentence. Any chance?..

You could not mistake the meaning of ‘fight’ here.

‘to fight with’ is a little ambiguous.
It could mean ‘to fight alongside’ or could mean ‘to fight against’.