I am not sure is that was a planned maneuver. "La Migra" has been limiting immigration from Mexico by the means that would make Adolf Hitler proud, and nobody but a handful of civil rights activists gives a shit about it. If I recall (correct me if I'm wrong), the US and Cuba have an immigration agreement reached after the boat lift crisis, which basically stipulates that all illiegal immigrants be returned to Cuba.
I suspect a more mundane scenario - the INS got a case and did not know what to do about it. If they went by the book and returned the boy, they would be criticized for sentimental reasons. I bet they saw the writing on the wall, or more precisely, headlines in mainstream rags "Little cute victim and orphan expelled, returned to a Communist dictatorship." If they tried to keep him here, they would be required to find foster care and overcome thousands of bureaucratic hurdles erected by GOP fascists to "keep immigrants out of the welfare system." So turning him to his distant relatives was a classical case of bureaucratic off-loading a problem they did not how to handle - it would have have "worked" as it always does, except that the case developed unofereseen consequences.
Once the shit hit the fan, diffrent stakholders started defining the case in its own terms and use as rationalziation of their own political stakes that had nothing to do with the boy himself. This is a textbook example of the "garbage can" theory of organizatinal behaviour.
wojtek