Normally, the multiple FMGCs do their own individual position calculations and, being separate units, may well use different VORDMEs for their calculations.
On the SELECTED NAVAIDS page, the MCDU will show what navaids are tuned by its onside FMGC at the momenent, so if one decided to have both MCDUs display said page for a while inflight, it would be possible to compare the two sides automatic selections.
Back then, it was the Baglum (BAG) VOR in Turkey that caused the mapshifts. Is the identifier of the troublesome Iranian station known as well?