The description of the app on the website looks like snake oil.
By definition, lost information cannot be recovered. So what's this app doing? Creating random noise?
You use the terms "tinny, unbalanced, open, warm". The website uses the terms "wider, deeper, crisper, fuller". These are subjective terms which cannot be measured and mean different things to different people. It smells a lot like a (potentially very well done) equalizer.
That said, if the music sounds better to your ears, then great. Ultimately that's all that matters.
(This kind of stuff reminds me of the 24bit/192khz fad that started up a few years ago: people are paying a lot extra for these larger files and swearing they sound better even though physics & human physiology dictate there cannot be a discernible difference.)