Is giving AI agents DB access the new BI-tool problem?

A couple of early-to-mid-stage startups I'm consulting with are asking the same question: their AI/ML team wants production Postgres data, and nobody's quite sure how to give it to them.

I've handled this before for BI teams — read replica with a generous `max_standby_streaming_delay` and `hot_standby_feedback` on, accepting the occasional bloat on the primary. Worked fine. But the AI/ML ask feels different in ways I can't fully articulate yet, which is part of why I'm asking.

A few things I'm trying to calibrate:

Where does the agent actually connect? Primary with RLS, read replica, warehouse (Snowflake/BigQuery/Redshift), lakehouse (Iceberg/Delta on S3), or something else?

If you're not doing this — is it compliance, cost fear, bad experiences (runaway queries, PII in prompts), or something else?

And the one I'm most curious about: does this actually feel different from giving BI tools DB access, or is it the same problem wearing new clothes?

Not looking for product recommendations. Trying to get a real sense from people who've actually faced this challenge.