There is NO question that a device that measures better will sound more accurate(maybe not better depending on taste). The problem is we don't know how to measure audio products completely. We can do some measurements but the ones we do do not define a product. At minimum we need to do many measurements(and flatness and % distortion is far from sufficient) and also learn how to combine them for a final result. We can't do that now. The best we can do is identify measurements that are good clues and combine them with experienced listening however that's defined for each individual.
It is possible that some bad measurements can tell us that a product can't be accurate but we are miles from measurements totally defining accuracy. For what it's worth I am a measurements(and subjective person) and there are some measurements that I believe are good clues but they aren't the classical distortion and response ones. I recall my late friend Murray Zeligman who knew more about measurements than most tell me the first thing he looked at for a speaker was the impedance curve because it was a big source of predicting speaker performance.