In a word, yes.
Top down and left to right, SongBox cares about and prioritises your privacy and safety. To that end, (and despite being a tiny one man company with zero funding) SongBox has been built using world class infrastructure and services.
Infrastructure: SongBox is all built on Amazon's AWS cloud computing platform. You can read about that HERE.
Payments: SongBox is proud to utilise STRIPE, the world's most awesome payments platform. You can read about that HERE.
Other stuff: SongBox is born out of the frustration witnessed and experienced after 12 years in the music industry; it just wants to help. It's priced at a bare minimum to allow itself to launch, survive and hopefully grow. SongBox does things by the book and then some (when it feels the book just doesn't go far enough). SongBox pays it's taxes (if and when it makes any profit). SongBox looks after your data and promises never to give it away to any other companies. When you leave SongBox your data and assets are incinerated.
To reiterate, yes - you can trust SongBox.