One of the largest classes of digital assets are personal files on individual phones and other personal computers. So yes, sometimes you do very clearly own digital assets (and no, a link about one time where some government broke the law and stole someone's files doesn't refute that).

Your personal photos on your PC are digital, they're a digital asset, and you do own them. No contract necessary. The same is true for all sorts of other types of personal digital files you might hold as personal property, from spreadsheets to backup email records to pdf files of contracts and on it goes.