Oh yes I absolutely agree that the J-test is not diagnostic. If there are spuriae then it is unknown where the jitter came from. All it says is that the DAC failed to produce the digital test signal properly - it could be jitter or it coyld intermodulation distortion or both.
However, if a device passes the J-test with perfect results then one can only conclude that all distortion spuriae including any jitter of any sort are all below the noise floor.
Devices that pass this test perfectly are indeed rare which is why I agree that most DACs need a reclocker.