MOSCOW, June 14 -- The trucks crossed the line that almost nothing else does. While the front in eastern Ukraine stayed locked in its grinding stalemate, Russia handed back the remains of 1,212 Ukrainian soldiers this week, the latest in a chain of exchanges that has quietly become the one working channel between two governments that agree on little else.

In return, Russian officials said, Moscow received the bodies of 27 of its own. The lopsidedness of that count is its own kind of message, and each side reads it differently. Russia presents the exchanges as evidence of its good faith, a humanitarian track it has kept open even as the fighting intensifies. Ukraine treats the same numbers with grief and suspicion, wary of how remains are...