Fully agreed - our recommendation is to /not/ run your prod Postgres db yourself, but use one of the many great dedicated options out there - Crunchy Data, Neon, Supabase, or AWS RDS..!
It really depends upon how much data you have. If its enough to just dump then go crazy. If it isn't its a bit more trouble.
Regardless, you're going to have a much easier time developing your app if your datastore access latency is submillisecond rather than tens of milliseconds.
You're running at a pretty small scale if running your database locally for sub-milisecond latency is practical. The database solution provided by the DBA team in a data center is going to have about the same latency as RDS or equivalent. Typical intra-datacenter network latency alone is going to be 1-3ms.
They were talking about using things like Supabase, not just RDS.
Also, "small scale" means different things to different people. Given the full topic at hand, I would call it "nano scale". Depending upon your specific schema, you can serve tens of thousands of queries per second with a single server on modern hardware, which is way more than enough for the vast majority of workloads.