If you run it in a sandbox with no internet access and a read-only role login for the database, and you supervise it, how big is the risk do you reckon?

Of course there's an issue if the data in the database is contractually restricted and you don't have a zero retention endpoint for inference, but the former usually comes with the budget to fund the latter.

You think they're talking about giving them access to a live prod db/app? You know offline copies are a thing right?