Yes but the USSR was not a signatory to the Berne Convention in those days. Therefore USSR copyrights were not recognised in the west and western copyrights were not recognised in the USSSR. Therefore, Kenny Ball would have been legally entitled to claim composer royalties on Moscow Nights and the legitimate composers would have had no redress.
I imagine that, since the collapse of the USSR, Russia has now signed up to the convention. If so, that may explain why the piece is now copyright to its authors.