It depends on how you define "make stuff sound better". They aren't promising that it will sound better than the original file, rather it is supposed to sound better than what has been delivered to the end customer in the past.
Actually, I think one of the benefits of MQA is that it could make the result better due to incorporating the timing elements of the ADC in the encoding. That is, you could take one of Marks 24/96 files and play it back through a Meridian 861 + DSP 7200SE and it would not sound as good as that same file encoded by MQA and then decoded by that same MQA-enabled Meridian setup.
Why? Because with MQA, the timing errors introduced by the specific ADC box used by Mark are known and modeled, this info is used by the encoder to 'convolve' in the temporal domain the timing data that the decoder can then use to achieve that high temporal resolution.
So yes, I think the process enables the opportunity for it to sound better.