Doesn't Diplomatic Immunity only mean "immunity from prosecution"? So if a diplomat pulled out a gun to shoot someone, the police could tackle him or her and take the gun away, but there would be no prosecution for assault/attempted murder, just a deportation. They wouldn't stand by and watch the murder happen.
So in this case, I think the DC police could have (and should have) stopped the thugs, given them a bit of a pounding themselves, then sent them packing, no?
Secret Service may not get diplomatic immunity (though maybe immunity from prosecution for official acts, depending on the host country), but the State Department's Diplomatic Security Service do, AFAIK; so the thugs were probably members of Turkey's equivalent service, and if so probably do have diplomatic immunity.