I don't think it's that simple, I manage to shoot at 1/60th with flash and I don't get motion blur or double exposures. The problem I see is when people are setting the camera up to expose for ambient and then adding flash. Iso 6400 and flash? Sounds like the iso was more the issue than the shutter speed.
1/60th, with bounced flash as the main light on the subject:
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_MG_4214-Edit.jpg by tltichy, on Flickr
+1 on this....