In some cases, dual-nationality does not remove the obligation for national service in one or other of the countries, particularly where the country of origin requires a mandatory period of national service. Presumably not both at the same time, though. I can think of Israel, Greece (Cypriot) and Germany for starters as examples of people I have known where this has happened. I suspect that legally only having asylum status would prevent this? I am thinking particularly of the Iraqis who fled the Ba'ath regime between GW1 and GW2.
One question though, if you were coming to the end of mandatory enagement and your unit was deploying, would you volunteer to return to fight alongside your mates or disappear back to a safer country? It's a thorny one. Moreover, I suspect the statement by Fox3 may have been a media oversimplification:
In the first press release it notes that he wanted to 'know what it would be like in the Army'.
It may well be the case that the right to hold an Israeli passport (and of the Israelis I have known outside of that country, none were willing to give it up the entitlement) may well be dependent on certain criteria being fulfilled including National Service.