Now mini-NAS for backups of backups? That would make sense to me if you do not trust whomever is managing your administrative and backup servers. It might not even be full backups but one could at least back up the data critical to the business that your team is responsible for. A development team lead could automate more frequent backups to their mini-nas than the company has implemented for the wider audience use cases. That would not even need to be in the data-center unless your privacy, compliance and security teams say otherwise. Your home grown solution will still need really good physical security as random contract janitor can just walk out of the building with all of your intellectual property. The NAS just needs a very fast low latency connection to the data-center.
In my experience the revenue impacting data storage and flows should always be on the corporate maintained infrastructure unless one really wants to stand in front of the C-levels explaining why all the data was lost of a home grown implementation. Ideological and technical issues aside the optics will be awful. I've seen people walked out of companies for much less. Augmenting the corporate systems on the other hand can be a life saver especially if you know what data is critical to revenue flows and how many snapshots and full backups would keep your teams workflows uninterrupted. As an augmentation your systems could save the day and your team would look really sharp. As a side note, when your team does save the day by going above and beyond ensure that your management write up your team for awards. That can reduce management friction in the future and buy some leniency for mistakes that will inevitably occur.